LABORATORY  EXERCISES 


IK 


PHYSICAL    CHEMISTRY. 


BY 


FREDERICK   H.  GETMAN,  PH.D. 

Lecturer  in  Physics,  Columbia  University, 
Formerly  Carnegie  Research  Assistant,  Johns  Hopkins  University. 


SECOND  EDITION,  REVISED. 
FIRST  THOUSAND. 


NEW  YORK: 

JOHN  WILEY  &  SONS. 

LONDON:  CHAPMAN   &  HALL,  LIMITED. 

1908. 


Copyright,  1904,  1908? 

BY 

FREDERICK  H.  GETMAN. 


DRUMMOND,  PRINTER,  NEW  YORK. 


PEEFACE. 


WITH  the  growth  of  a  new  science  between  physics  and 
chemistry  there  has  arisen  need  for  a  new  type  of  laboratory 
manual.  This  need  has  been  met  by  two  books — Ostwald's 
"  Physiko-Chemische  Messungen "  and  Traube's  "Physi- 
kalisch-Chemische  Methode."  .Notwithstanding  the  excel- 
lence of  these  books  they  have  not  proven  themselves  prac- 
tical guides  in  the  laboratory,  owing  to  too  great  detail  and 
too  many  references  to  the  literature.  With  the  wish  to 
prepare  a  manual  which  may  be  placed  in  the  hands  of  the 
student  of  physical  chemistry,  the  author  has  written  this 
book.  He  would  state  at  the  outset  that  he  in  no  way  con- 
siders this  as  an  effort  to  rival  either  of  the  above  books, 
which  for  long  must  remain  the  standard  works  of  reference 
on  physico-chemical  measurements.  The  effort  has  been 
made  to  select  only  such  exercises  as  are  typical,  and  where 
several  different  methods  exist  for  the  measurement  of  the 
same  quantity,  only  in  rare  instances  has  more  than  one 
been  given.  In  a  word,  the  book  has  been  made  as  con- 
densed as  possible  in  order  not  to  discourage  the  student 
with  too  many  methods. 

It  has  been  thought  advisable  to  include  several  exer- 
cises which  are  usually  studied  in  physics,  but  these  may 
be  omitted  if  the  student  has  already  had  sufficient  practice 
with  them. 


IV  PREFACE. 

For  the  convenience  of  the  student  there  are  appended 
tables  of  various  physical  constants  which  may  be  of  ser- 
vice hi  the  laboratory. 

For  the  kind  assistance  given  by  friends  the  author 
would  acknowledge  his  thanks,  and  especially  to  Prof.  W. 
0.  At  water,  who  has  so  generously  placed  at  his  disposal 
the  material  for  the  section  dealing  with  the  determination 
of  heats  of  combustion.  To  Messrs.  P.  Blakiston's  Son  &  Co. 
I  would  express  my  thanks  for  permission  to  use  several  illus- 
trations from  Traube's  "  Physico-Chemical  Methods." 

If  this  book  finds  a  place  for  itself  in  the  hands  of  the 
student  beginning  the  study  of  physical  chemistry  and 
proves  to  be  of  real  service  to  him,  it  will  have  accomplish- 
ed all  that  the  author  might  wish. 

FREDERICK  H.  GETMAN: 

BALTIMORE,  MD.,  April,  1904. 


PREFACE  TO  SECOND   EDITION. 


As  a  foreword  to  the  revised  edition  of  this  manual  the 
author  would  call  attention  to  the  insertion  of  a  chapter  on 
thermostats  and  to  the  enlargement  of  the  chapters  treating 
of  electromotive  force,  solubility  and  chemical  dynamics. 

A  brief  outline  is  given  of  methods  for  the  measurement 
of  radioactivity,  and  several  other  chapters  have  been  modi- 
fied to  conform  with  modern  laboratory  requirements. 

It  is  hoped  that  in  its  present  form  the  book  may  prove 
of  service  as  a  guide  to  the  methods  of  physico-chemical 
research. 

In  conclusion,  the  author  would  record  his  deep  sense 
of  obligation  to  his  readers  for  their  suggestions  and  criti- 
cisms, and  gladly  accords  them  credit  for  any  changes 
which  may  make  this  edition  superior  to  the  former. 

FREDERICK  H.  GETMAN. 

COLUMBIA  UNIVERSITY, 

New  York  City,  January  18,  1908. 


TABLE  OF  CONTENTS. 


INTRODUCTORY  MEASUREMENTS. 
CHAPTER  I. 

PAGE 

WEIGHING 1 

Care  of  Balance.  Weighing  by  Vibrations.  Sensitiveness  of  a 
Balance.  Inequality  of  Arms  of  the  Balance.  Reduction  of  Weigh- 
ings to  Vacuo.  Calibration  of  a  Set  of  Weights. 

CHAPTER  II. 

VOLUME  AND  DENSITY ..... .v.     13 

Apparatus  for  Measuring  Volumes.  Calibration  of  Measuring- 
flasks.  Calibration  of  Burettes.  Calibration  of  a  Eudiometer. 
Density  (Specific  Gravity).  Density  of  Solids.  Density  of  Liquids. 
Density  of  Gases  (Vapor  Density).  Method  of  Dumas.  Method 
of  Victor  Meyer. 

CHAPTER  III. 

THERMOSTATS 34 

The  Tank.  The  Bath.  The  Temperature  Regulator.  The 
Stirrer.  The  Heater. 

CHAPTER  IV. 

VISCOSITY  AND  SURFACE  TENSION -..-..-.  . . . 42 

Flow  of  Fluid  through  a  Long  Tube.  Measurement  of  the  Coeffi- 
cient of  Viscosity.  Method  of  Poiseuille.  Method  of  Coulomb. 
Surface  Tension.  Measurement  of  Surface  Tension.  Relation  be- 
tween Surface  Tension  and  Molecular  Weight. 

vii 


Viii  TABLE  OF  CONTENTS. 

THERMAL  MEASUREMENTS. 
CHAPTER  V. 

PACK 

THERMOMETRY 56 

The  Mercury  Thermometer.  Comparison  of  a  Thermometer  with 
a  Standard  Thermometer.  Calibration  by  Means  of  a  Series  of 
Fixed  Temperatures.  Correction  for  Unheated  Stem.  The  Fixed 
Points  of  a  Thermometer.  Expansion.  Determination  of  the 
Coefficient  of  Cubical  Expansion  of  Glass  and  Liquids.  Molecular 
Volumes  of  Liquids  at  their  Boiling-points. 

CHAPTER  VI. 

MELTING  AND  BOILING-POINTS 67 

Melting-point.  Boiling-point.  Depression  of  the  Freezing-points 
of  Solvents  by  Dissolved  Substances.  Apparatus  and  Method. 
Dissociation  by  the  Freezing-point  Method.  Elevation  of  the  Boiling- 
points  of  Solvents  by  Dissolved  Substances.  Apparatus  and 
Method.  Molecular  Weight  by  the  Method  of  Longinescu. 

CHAPTER  VII. 

CALORIMETRY 83 

Quantity  of  Heat.  Specific  Heat.  Determination  of  the  Specific 
Heat  of  Solids.  Heating  Vessel.  The  Calorimeter.  Method  of 
Operation.  Loss  of  Heat  by  Radiation.  Loss  of  Heat  to  Calorime- 
ter. Loss  of  Heat  to  Stirrer.  Loss  of  Heat  to  Thermometer. 
Determination  of  the  Specific  Heat  of  Liquids.  Heat  of  Fusion. 
Heat  of  Vaporization.  Thermo-chemistry.  Heat  of  Neutralization. 
Heat  of  Solution.  Heat  of  Hydration.  Heat  of  Dilution.  Heat 
of  Combustion.  Heat  of  Formation. 

OPTICAL  MEASUREMENTS. 

CHAPTER  VIII. 

THE  SPECTROSCOPE 129 

Adjustment  of  the  Spectroscope.  Reduction  of  Scale-readings  to 
Wave-lengths.  Absorption  Spectra.  Spectrophotometry.  Appa- 
ratus of  Kriiss.  Method  of  Operation.  Refractive  Indices.  The 


TABLE  OF  CONTENTS.  ix 

PAGE 

Pulfrich  Refractometer.  Refraction  Constants.  The  Polarimeter. 
The  Laurent  Polarimeter.  The  Lippich  Polarimeter.  Lamp  for 
Homogeneous  Light.  Observing  Tubes.  Specific  Rotation. 
Molecular  Rotation.  Rotation  Dispersion. 


ELECTRICAL  MEASUREMENTS. 

CHAPTER  IX. 

ELECTRICAL  UNITS 154 

Sources  of  Current. 


CHAPTER  X. 

RESISTANCE  (CONDUCTIVITY) 159 

Specific  and  Molecular  Conductivity.  Resistance  Boxes.  Wheat- 
stone's  Bridge.  Calibration  of  the  Bridge-wire.  Conductivity  Cells. 
Induction  Coil  and  Telephone.  Resistance  Capacity  of  the  Cell. 
Carrying  out  a  Measurement.  Pure  Water.  Equivalent  Conduc- 
tivity. Degree  of  Dissociation.  The  Dissociation  Constant.  The 
Basicity  of  Acids.  Solubility  by  the  Conductivity  Method. 


CHAPTER  XI. 

ELECTROMOTIVE  FORCE 183 

Clark  Standard  Cell.  Temperature  Coefficient.  Weston  Standard 
Cell.  Helmholtz  One-volt  Cell.  Lippmann  Electrometer.  Use  of 
the  Capillary  Electrometer.  The  Measurement  of  Electromotive 
Force,  Potential  Differences.  Normal  Electrodes.  Preparing  the 
Electrodes.  Measurement  of  the  Potential  Difference  between  a 
Metal  and  a  Solution  of  a  Salt  of  the  Metal.  Concentration  and 
Potential  Difference.  Concentration  Cells  Involving  Ionic  Migration. 
Solubility  from  E.M.F,  Measurements.  Gas  Cells. 


CHAPTER  XII. 

MEASUREMENT  OF  CURRENT  AND  TRANSPORT  NUMBERS 209 

The    Silver    Voltameter.     The    Copper    Voltameter.     Transport 
Numbers, 


x  TABLE  OF  CONTENTS. 

CHAPTER  XIII. 

PAGE 

MEASUREMENT  OP  DIELECTRIC  CONSTANTS  AND  RADIOACTIVITY 219 

Apparatus  of  Nernst.  Carrying  out  a  Determination.  Measure- 
ment of  Radiocativity.  The  Wilson  Electroscope.  The  Electrom- 
eter. Testing  Vessel.  Battery.  Electrometer  Key.  Measurement 
of  lonization  Current. 

DYNAMICAL  MEASUREMENTS. 

CHAPTER  XIV. 

SOLUBILITY 235 

Determination  of  Solubility.  Partition  of  a  Solute  between  Two 
Non-miscible  Solvents. 

CHAPTER  XV. 

CHEMICAL  KINETICS 242 

Reaction  of  the  First  Order.     Inversion  of  Cane-sugar.     Catalysis 
of  Methyl  Acetate.     Reaction  of  the  Second  Order.     Saponification 
of  Ethyl  Acetate.     Transition  Points.     Solubility  Method.     Ten- 
simetric  Method.     Dilatometric  Method.     Electrical  Method. 

TABLES 259 

Reduction  to  Vacuum  of  Weighings  made  with  Brass  Weights  in 
Air.  Density.  Density  of  Water.  Volume  of  Water  from  0°  to 
31°.  Surface  Tension  of  Liquids  in  Contact  with  Air.  Viscosity  of 
Liquids.  Reduction  of  Gas  Volumes  to  0°  and  760  mm.  Reduction 
of  Barometer  Readings  to  0°.  Reduction  of  Mercury-in-glass 
Thermometer  Readings  to  the  Normal  Hydrogen  Scale.  Vapor 
Pressure  of  Water.  Vapor  Pressure  of  Mercury.  Table  for  the 
Conversion  of  the  Thermometer  Readings.  Specific  Heats,  Heats 
of  Fusion,  and  Melting-points  of  the  Elements.  Coefficients  of 
Expansion,  Specific  Heats,  Melting-points,  and  Boiling-points  of 
Liquids.  Boiling  Temperature  t  of  Water  at  Barometric  Pressure 
6.  Correction  for  Temperature  of  Mercury  in  Thermometer-stem. 
Wave-lengths  of  Lines  of  Solar  Spectrum  in  Air  at  18°.  Table  for 
Wheatstone's  Bridge.  Table  for  Calculating  the  Dissociation  Con- 
stant. Table  of  International  Atomic  Weights.  Logarithms  of 
Numbers, 


LABORATORY  EXERCISES 

IN 

PHYSICAL  CHEMISTRY. 


INTRODUCTORY. 

MEASUREMENTS. 


CHAPTER  I. 
WEIGHING. 

WEIGHING,  or  the  comparison  of  masses,  is  one  of  the 
fundamental  and  most  common  operations  of  the  physico- 
chemical  laboratory.  For  this  reason  great  care  should  be 
exercised  to  secure  a  high-grade  balance  (Fig.  1)  and  set  of 
weights  (Fig.  2).  Among  the  points  to  be  given  attention 
in  the  selection  of  a  balance  are  the  following: 

1.  When    the   beam   is   repeatedly    stopped    and    again 
released  it  must  invariably  assume  the  same  position. 

2.  When   the   beam  is   swinging  the  amplitude   of   the 
vibrations  must  diminish  slowly. 

3.  Upon   arrestment   the  pointer  should   stand  directly 
over  the  middle  division  of  the  scale. 

4.  When  the  beam  is   released   the  points    of   support 
should  act  in  unison. 


MEASUREMENTS. 


Theee  four  conditions  must  hold  equally  well  when  the 
pans  are  loaded  with  the  maximum  weights  for  which  the 
balance  is  designed. 


FIG.  1. 


5.  The  arms  should  be  of  equal  length. 

6.  The  device  for  moving  the  rider  must  be  provided 
with  stops  to  prevent  striking  the  beam. 


WEIGHING.  3 

7.  The  arrestment  should  work  smoothly,  and  the  doors 
to  the  balance-case  must  run  freely. 

8.  The  pointer  must  move  close  to  the  scale. 

9.  The  divisions  of  the  scale  should  be  about  one  milli- 
metre. 

Care  of  the  Balance. — -The  balance  should  stand  on  a 
firm  table,  or  preferably  on  a  stone  slab  resting  upon  masonry 
piers.  It  should  not  be  exposed  to  the  direct  rays  of  the 


E 

i"  c 

«  JT 

c  "•  in 

FIG.  2. 

sun  or  to  the  direct  radiation  from  any  source  of  heat.  Care 
must  be  taken  as  to  the  position  of  gas-flames,  since  a  gas- 
flame  a  few  feet  from  a  delicate  balance  is  sufficient  to  de- 
stroy the  accuracy  of  the  weighings.  After  the  position  of 
the  balance  has  been  determined  it  is  levelled,  and  then 
should  be  disturbed  as  little  as  possible.  To  protect  the 
instrument  from  rust  and  to  exclude  the  influence  of  hygro- 
scopic moisture  during  weighing,  a  small  bottle  of  calcium 
chloride  is  frequently  placed  inside  the  balance-case.  The 
knife-edges  and  the  pans  should  occasionally  be  cleaned 
with  a  fine  cameFs-hair  brush.  Weights  should  be  placed 
on  the  pans  only  when  the  balance  is  arrested,  and  likewise 
when  weights  or  the  object  to  be  weighed  are  removed  the 
beam  should  be  stopped.  Care  should  be  taken  to  place  the 
weights  as  nearly  in  the  centre  of  the  pan  as  possible,  and 


4  MEASUREMENTS. 

the  pans  should  not  be  allowed  to  swing  while  making  a 
weighing. 

After  weighing  with  heavy  weights  the  zero-point  must 
be  redeter mined.  When  making  the  final  weighings  the 
balance-case  must  be  shut.  Hot  bodies  must  under  no  cir- 
cumstances be  introduced  into  the  balance-case.  All  sub- 
stances likely  to  injure  the  pans  must  be  weighed  in  closed 
vessels. 

The  weights  furnished  with  a  high-grade  balance  are 
made  of  brass  and  platinum.  The  larger  weights  are  of 
brass,  either  gilded  or  platinized,  while  the  smaller  weights 
are  of  plat  mum.  Care  should  be  taken  to  protect  these 
weights  from  contact  with  mercury  or  any  corrosive  liquid. 
The  weights  should  be  handled  only  with  the  pincers,  and 
should  be  returned  to  their  places  in  the  box  immediately 
after  using. 

Weighing  by  Vibrations. — The  first  step  in  making  a 
weighing  by  the  method  of  vibrations  consists  in  determining 
the  zero-point,  or  the  point  at  which  the  pointer  comes  to 
rest  when  the  beam  is  unloaded.  Since  it  would  demand 
too  much  time  to  wait  for  the  beam  to  come  to  rest,  we 
determine  the  zero-point  by  observing  the  extreme  positions 
of  the  pointer  when  swinging.  Where  only  moderate  accu- 
racy is  required  it  is  sufficient  to  determine  two  suc- 
cessive turning-points  and  to  take  their  arithmetical  mean. 
If  greater  accuracy  is  desired,  several  turning-points  are 
observed,  taking  care  for  the  sake  of  reduction  that  an 
uneven  number  of  observations  is  made.  Five  or  seven  are 
amply  sufficient.  We  then  take  the  arithmetical  mean  of 
the  first,  third,  fifth,  and  seventh  observations,  and  of  the 
second,  fourth,  and  sixth,  and  finally  take  the  mean  of 
these  two  means.  This  is  the  required  zero-point. 

Care  should  be  taken  to  distinguish  readings  to  the  left 


WEIGHING.  5 

by  a  negative  sign,  or  the  middle  point  of  the  scale  may  be 
called  10  instead  of  0,  and  thus  negative  signs  avoided. 

Having  obtained  the  zero-point  we  place  the  body  to  be 
weighed  on  one  of  the  scale-pans,  and  bring  the  beam  nearly 
to  the  zero-point  by  means  of  weights  placed  on  the  other, 
and  finally  by  moving  the  rider  along  the  beam. 

Now  make  another  series  of  readings  as  above,  then 
remove  or  add  weights  (one  or  more  milligrams)  according 
as  the  weights  were  too  heavy  or  too  light,  until  the  position 
of  equilibrium  falls  on  the  other  side  of  the  zero-point,  and 
determine  it  by  again  observing  the  swings  of  the  pointer. 
From  these  data  we  may  calculate  the  weight  of  the  body, 
W.  Suppose  the  zero  to  have  been  a,  and  with  the  weight  u 
let  the  new  zero-point  be  denoted  by  b,  while  with  the  weight 
v  let  the  corresponding  zero-point  be  expressed  by  c.  Then, 
since  for  small  deflections  the  difference  of  the  positions  of 
equilibrium  is  proportional  to  the  difference  of  the  weights, 
we  have 

a—c    W  —  v 
b  —c     u  —  v' 
therefore 

}fr_fl+ («_„)*_£ 

u      C 

Due  regard  must  be  paid  to  the  signs,  for  which  reason  it  is 
simpler  to  number  the  scale-divisions  as  suggested  above. 

Illustration. — The  value  of  the  zero-point  has  been  found 
to  be  9.74. 


Weight, 
me?. 

Turning-point. 

Mean. 

Point  of 

T>                   A 

3036 

7.8 

7.8 

7.9 

7.83 

Jtvest. 

9.04 

10.3 

10.2 

10.25 

3037 

9.5 

9.4 

9.3 

9.40 

9.95 

10.5 

10.5 

10.50 

6  MEASUREMENTS. 

Deviation  for  1  mg.  =  0.91  scale-division;  hence,  applying  the 
formula,  we  have 

W  =  3036  +  ~^p  =  3036.77. 

The  amplitude  of  swing  should  amount  to  about  three  or 
four  scale-divisions.  Care  should  be  taken  to  record  the 
observations  as  given  above. 

Sensitiveness  of  a  Balance. — The  difference  of  indication 
for  1  mg.  difference  in  weight  is  known  as  the  sensitiveness  of 
a  balance. 

This  quantity  is  an  important  factor  in  determining  the 
excellence  of  a  balance,  and  a  knowledge  of  it  may  be  used 
to  simplify  the  process  of  weighing. 

The  method  of  determining  this  quantity  is  at  once 
apparent.  The  load  for  which  the  sensitiveness  is  sought  is 
placed  in  each  pan,  and  into  one  pan  a  small  excess,  so  that 
the  pointer  is  displaced  about  three  divisions  from  the  posi- 
tion of  equilibrium. 

This  position  is  determined  accurately  by  means  of  the 
method  of  oscillations;  let  us  suppose  it  to  be  a.  Now  by 
adding  w  milligrams  to  the  other  pan  the  position  of  equi- 
librium is  to  be  brought  nearly  as  far  on  the  other  side  of 
the  centre  and  observed  as  before.  Let  this  position  be 

denoted  by  b.     The  sensitiveness  is  then  -    - .     This  quan- 

w 

tity  should  be  determined  for  different  loads  at  intervals  of 
10  grs.,  and  the  results  plotted  on  coordinate-paper,  loads 
as  abscissae  and  sensitiveness  as  ordinates. 

The  sensitiveness  can  be  increased  or  diminished  by 
means  of  a  movable  weight,  which  can  be  screwed  up  or 
down  as  desired.  The  time  of  vibration  is  a  direct  function 
of  the  sensitiveness,  and  should  ordinarily  be  from  10  to  15 


WEIGHING.  7 

seconds.  From  the  curve  of  sensitiveness  we  may  gain 
assistance  in  weighing.  Thus  let  us  suppose  that  during  a 
weighing  the  pointer  is  displaced  10  divisions  from  its  posi- 
tion of  equilibrium  toward  the  right  hand  and  let  the  load 
be  150  grams;  then  from  the  sensibility  curve  we  learn  that 
the  sensitiveness  corresponding  to  this  load — that  is,  the  dis- 
placement for  1  mg. — is  25.  Therefore  |f  or  0.4  of  a  milli- 
gram is  the  amount  which  must  be  added  to  the  weights  in 
order  that  they  may  counterbalance  the  body. 

Inequality  of  the  Arms  of  the  Balance. — This  effect  may 
be  eliminated  by  two  methods,  known  as  those  of  Borda  and 
of  Gauss. 

(a)  Method  of  Borda. — The  body  to  be  weighed  is  coun- 
terbalanced by  weights,  shot,  etc.,  and  finally  brought  as 
near  the  position  of  equilibrium  as  possible  by  means  of 
fine  sand,  bits  of  paper,  or  other  suitable  substances.  The 
body  is  now  removed  and  replaced  by  standard  weights, 
until  the  balance  is  once  more  in  equilibrium.  The  weight 
in  the  pan  will  now  truly  represent  the  weight  of  the  body, 
since  each  has  been  placed  under  similar  conditions.  In 
using  this  method  it  is  advisable  to  weigh  by  vibrations. 

(6)  Method  of  Gauss. — This  method  consists  in  weighing 
the  body  first  in  one  pan  and  then  in  the  other.  Let  us 
suppose  that  a  body  of  which  the  true  weight  is  W  weighs 
A  when  placed  in  the  right-hand  pan  and  B  when  placed  in 
the  left-hand  pan.  If  we  denote  by  R  and  L  the  lengths 
of  the  right  and  left  arms  of  the  balance,  then  we  have 

WR=AL 
and 

WL=BR-, 
therefore 

W2=AB, 


8  MEASUREMENTS. 

or 


From  this  we  learn  that  the  true  weight  is  the  geometri- 
cal mean  of  the  apparent  weights. 

Since  we  generally  find  A  and  B  to  be  very  nearly  equal, 
no  serious  error  is  introduced  by  taking  the  arithmetical 
instead  of  the  geometrical  mean.  Of  the  two  methods,  that 
of  Gauss  is  to  be  preferred,  since  it  consumes  less  time  and 
gives  more  accurate  results. 

Reduction  of  Weighing  to  Vacuo.  —  For  the  accurate 
comparison  of  masses  it  is  essential,  when  the  weighing  is 
made  in  air,  that  their  densities  be  the  same.  For  this 
reason,  unless  the  body  weighed  has  the  same  density  as 
the  standard  weights  employed,  an  error  will  be  introduced. 
The  reason  is  that  if  the  body  and  the  weights  are  of  un- 
equal volume,  they  will  displace  different  amounts,  of  air 
and  hence  lose  weight  unequally. 

A  correction  for  this  may  be  easily  deduced. 

Let  7,  M}  and  A  denote  the  volume,  mass,  and  density 
of  the  body,  while  v,  m,  and  d  have  similar  significations  with 
respect  to  the  weights.  These  quantities  are  so  related  that 

M  m 

V=—r    and     v  =  -*-. 
A  o 

Since  every  body  loses  in  air  the  weight  of  the  volume 
which  it  displaces,  it  follows  that  the  body  to  be  weighed 
loses  XV  and  the  weights  to,  where  X  is  the  density  of  the  air. 
Since  the  weights  after  subtracting  these  losses  are  equal, 
we  have 


or 


WEIGHING. 

On  account  of  the  smallness  of  A  in  comparison  with  J  or 
we  may  write 


1— •"• 

Illustration. — The  correction  of  the  apparent  weight  m 
of  a  quantity  of  water  when  weighed  with  brass  weights 
(d  =  8A)  amounts  to 


m 


0.0012/j-;r^j=ra- 0.00 106,  or  1.06  mg.  for  every  gram. 


Calibration  of  a  Set  of  Weights.* — In  correcting  a  set  of 
weights  as  many  weighings  must  be  performed  as  there  are 
weights  to  be  corrected.  From  these  data  a  series  of  equa- 
tions are  formed  from  which  the  ratio  of  the  arms  of  the 
balance  and  that  of  the  weights  to  each  other  or  to  a  con- 
venient unit  may  be  deduced. 

With  the  set  of  weights  used  in  analysis  the  following  is 
the  mode  of  procedure: 

The  larger  weights  are  distinguished  as 

50',    20',    10',    10",    5',    2',    r,    1",    V". 

A  double  weighing  is  performed  with  50'  on  one  side  and 
the  rest  of  the  weights  on  the  other.  Suppose  it  has  been 
found  that  the  balance  is  in  equilibrium,  i.e.,  the  pointer  is 
in  the  same  position  as  when  the  balance  is  unloaded,  when 

Left.  Right. 

50'  20'+ 10'+  ...  +rmg. 

20'+ 10'+ 10'+  . . .  + 1  mg.  50' 

*  From  Kohlrausch's  Introduction  to  Physical  Measurements. 


10  MEASUREMENTS. 

Then  the  ratio  of  the  arms  of  the  balance  is 

EL_          l-r 
L~    + 100,000' 
and 

50' =  20'+ 10"+  ...  +  ^tl 

r> 

When  j-  has  been  determined  a  single  weighing  is  sufficient 
for  the  other  weights;  for  a  weight  p,  on  the  right-hand  pan, 

r> 

is,  on  account  of  the  length  of  the  arms,  reduced  to  p-j 

when  weighed  on  the  left  hand. 

Example.— Let  r=  -0.83,  1  =  2.53: 

50'  =  20'  + 10'  + 10"  +  5'  + 1'  + 1"  + 1'"  +  0.85  mg., 
and 

-=1.0000336. 

Further,  if  it  be  found,  when  comparing  20'  with  10' +10", 

Left.  Right, 

that  20'  + 0.91  mg.  10' +10" 

keeps  the  balance  in  equilibrium,  in  a  balance  with  equal 
arms  the  equal  weights  would  be 

20' +  0.91  and  (10' +10")  1.0000336, 
or 

10' +10"  + 0.67  mg. 

Suppose  that  from  five  weighings  we  have  found 

50'  =20'+ 10'+  . ..  +A, 
20'  =10' +10"  +B, 

10"  =  10'  +(7, 

1'  +!"+!'"  =  10'  +  D, 


WEIGHING.  11 

where  of  course  A,  B,  (7,  D  may  be  either  positive  or  nega- 
tive. From  these  equations  the  values  of  the  five  weights 
must  be  expressed  in  terms  of  some  unit — the  sum  of  the 
single  grams  being  provisionally  considered  as  one  weight. 
If  a  comparison  with  a  normal  weight  be  not  made  at  the 
same  time,  this  unit  is  so  chosen  that  the  correction  of  the 
separate  weights  shall  be  as*  small  as  possible,  which  is  the 
case  when  we  consider  the  whole  sum  as  correct — i.e.,  when 
we  consider 

50' +  20' +10'+  .  .  .  =100,000  mg. 

Now  it  is  easily  found,  by  first  of  all  expressing  all  the 
weights  in  terms  of  10',  that 

50'  +  20'+10'  +  . .  .  =  10 -10'  +  A  +  2B  +  4(7+21)  =  100,000  mg. 

Calling,  therefore, 

A  +  2£  +  4<7+27) 

-JO"          -8, 

we  have  10' =10,000 mg.-  S, 

10"  =  10,000  "  -  S+C, 
5' +2' +...  =  10,000  "  --  S+D, 

20'  =20,000  "  -2S+B  +  C, 

50'  =50,000  "  -5S+A  +  B+2C+D, 

=  50,000  "  -\A. 

The  proof  of  the  correctness  of  the  numerical  work  is 
easily  found  from  the  above  to  be  that  the  sum  of  the  cor- 
rections when  expressed  as  numbers  must  be  equal  to  0  and 
the  equations  given  above  must  be  fulfilled. 

Again,  the  following  equations  having  been  obtained  by 
comparing  the  weights  5',  2',  1',  1",  V"  with  each  other: 
5'  =2'+l'+l"+l'"  +  a, 
2'  =!'+!"  +6, 

1"  =  !'  +c, 

!'"  =  !' 


12  MEASUREMENTS. 

As  in  the  previous  case,  calling 

a+2b+4c+2d+S-D 

-To" 

we  have  1'   =  1000mg.—  s, 

1"  =1000  "     -  s  +  c, 

1"'  =  1000  "   --  s  +  d, 

2'   =2000  "  -2s+b+c, 

5'   =5000  <f  -5s+a+b+2c+d. 

In  the  same  manner  we  proceed  with  the  smaller  weights, 
only  remarking  that  usually  the  inequality  of  the  arms  of 
the  balance  no  longer  needs  consideration. 

In  order  to  refer  the  table  of  errors  to  an  accurate  gram 
weight,  it  is  necessary  to  compare  the  weights,  or  one  of 
them,  with  a  normal  weight. 


CHAPTER  II. 


VOLUME  AND  DENSITY. 

Apparatus  for  Measuring  Volumes. — The  measurement 
of  volumes  is  most  satisfactorily  accomplished  by  means  of 
various  forms  of  graduated  vessels.  The  most  important 
of  these  are : 

(a)  Measuring-flasks  (Fig.  3). — These  are  made  so  as  to 
contain,  when  filled  to  a  certain  mark  and  at  a  definite 


Q 


FIG.  3. 


temperature,  a  definite  volume.  This  volume,  together  with 
the  temperature  for  which  the  flask  is  correct,  is  generally 
etched  upon  the  glass.  The  chief  sizes  used  hi  physico- 

13 


14 


MEASUREMENTS. 


chemical  work  are  1000  c.c.,  500  c.c.,  250  c.c.,  100  c.c.,  and 
50  c.c.  Occasionally  flasks  are  marked  with  two  lines,  one 
for  capacity  and  the  other  for  delivery. 


FIG.  4. 


FIG.  5. 


(&)  Pipettes. — These  are  tubes  open  at  both  ends — the 
one  opening  being  small,  while  the  other  is  large  enough  to 
be  covered  by  the  finger  (Fig.  4).  The  smaller  sizes  are 
made  of  straight  tubing,  while  the  larger  ones  have  a  bulb 
or  cylinder  hi  the  centre.  The  chief  sizes  are  100  c.c.;  50  c.c.; 


VOLUME  AND  DENSITY. 


15 


25  c.c.,  10  c.c.,  and  5  c.c.  Pipettes  of  50  c.c.  capacity  and 
graduated  into  cubic  centimetres  and  tenths  are  extremely 
useful.  Pipettes  are  filled  by  suction.  When  the  liquid 
has  reached  the  mark  the  larger  end  is  covered-  by  the 
finger  and  the  liquid  conveyed  and  delivered  without  loss. 

(c)  Burettes. — The  form  of  burette  best  suited  to  the 
physico-chemical  laboratory'  is  that  known  as  Mohr's  bu- 
rette. This  consists  of  a  graduated  tube  furnished  with  a 


I 


FIG.  6. 


FIG.  7. 


glass  stop-cock  at  the  lower  end  (Fig.  5).  The  most  conve- 
nient size  is  a  burette  of  50  c.c.  capacity  divided  into  tenths. 
The  best  readings  are  obtained  with  burettes,  which  are 
furnished  on  the  back  with  a  blue  enamel  strip  (Fig.  6)  on  a 
white  ground.  This  device  enables  the  observer  to  make  a 
very  sharp  reading,  \vhich  is  little  affected  by  parallax. 

(d)  Eudiometers. — These  are  graduated  tubes  closed  at 
one  end,  and  are  used  for  the  measurement  of  gases.  They 
are  graduated  into  cubic  centimetres  and  tenths  (Fig.  7). 


16  MEASUREMENTS. 

The  makers  of  apparatus  for  the  measurement  of  vol- 
umes generally  graduate  it  for  use  at  either  15°  C.  or  17°.5  C., 
these  temperatures  being  an  average  for  laboratory  tem- 
peratures. 

Calibration  of  Measuring-flasks.  —  No  measuring-vessel 
should  be  used  until  its  accuracy  has  been  tested.  To  verify 
the  accuracy  of  a  measuring-flask  it  is  first  cleaned  and 
thoroughly  dried  and  then  weighed.  It  is  then  filled  with 
water  up  to  the  mark,  the  inside  of  the  neck  being  dried, 
and  weighed  again.  The  temperature  of  the  water  must 
be  taken. 

This  weighing  must  now  be  corrected  (1)  for  dimin- 
ished density  of  the  water  due  to  excess  of  temperature  over 
4°  C.,  and  (2)  for  loss  of  weight  in  air. 

Denote  the  apparent  weight  in  air  by  IF,  and  let  A  be 
the  density  of  the  air.  Assume  the  density  of  the  brass 
weights  to  be  8.4.  The  volume  of  the  water  will  be  nearly 
W  c.c.,  and  it  will  lose  in  air  WX  grams,  while  the  weights 

will  lose    -.    The  total  loss  will  then  be 


WU-^)=0.881TfA, 

and  the  true  we  ght  of  water  will  be 
TF(1  +  0.88U). 

This  exact  weight  will,  however,  occupy  more  than 
TT(1  +  0.881A)  c.c.,  for  water  at  15°  C.  has  a  greater  volume 
than  at  4°  C.  From  the  tables  we  learn  that  1  c.c.  of  water 
at  4°  C.  occupies  1.000867  c.c.  at  15°  C.  Therefore  the 
actual  number  of  cubic  centimetres  contained  in  the  flask 
will  be 

W  (1+0.881  A)  1.000867. 


VOLUME  AND  DENSITY. 


17 


Calibration  of  Burettes. — All  graduated  tubes,  such  as 
burettes,  eudiometers,  etc.,  would  contain  equal  volumes  in 
equal  lengths  if  the  bore  of  the  tubes  were  uniform.  Since 
this  is  rarely  the  case,  the  errors  must  be  determined.  A 
small  calibration-gauge  is  attached  to  the  lower  end  of  the 


FIG.  8. 

burette.  This  gauge  (Fig.  8)  consists  of  a  small  pipette 
holding  1  or  2  c.c.  between  the  marks  a  and  b,  and  a  side 
tube  below  the  mark  a.  When  the  apparatus  is  perfectly 
clean  the  burette  and  side  tubes  are  filled  with  air-free 
distilled  water  and  the  level  brought  to  the  zero-division  by 
means  of  the  stop-cock  on  the  burette.  In  the  pipette  the 
water  is  run  out  to  the  mark  a  by  means  of  the  spring-clip  //. 


OF  THE 
t       IIMIUETDCITV 


18  MEASUREMENTS. 

Water  is  then  run  in  through  /  from  the  burette  until  the 
level  of  the  meniscus  is  at  6.  The  reading  of  the  burette  is 
then  noted.  The  water  is  next  run  out  through  //  until 
the  level  is  again  at  a,  then  run  in  through  /  up  to  b,  the 
second  reading  on  the  burette  being  noted,  and  so  on  until 
the  last  division  has  been  reached. 

The  readings  of  the  burette  then  give  directly  the  posi- 
tions at  which  the  contents  reckoned  from  the  zero-division 
are  equal  to  2,  4,  6,  8,  10,  ...  c.c.,  and  the  correction  at 
these  places  is  the  difference  between  the  two  values.  These 
corrections  should  be  written  down  on  a  sheet  of  heavy 
paper,  which  should  be  kept  with  the  burette,  or  the  results 
may  be  expressed  by  means  of  a  curve.  The  intermediate 
values  can  be  easily  ascertained  by  interpolation.  This 
same  method  of  calibration  may  be  applied  to  graduated 
pipettes. 

Calibration  of  a  Eudiometer. — The  method  of  calibration 
here  given  is  that  due  to  the  late  Professor  Bunsen.  The 
eudiometer  to  be  calibrated  is  fixed  firmly  in  a  vertical  posi- 
tion over  a  wooden  tray  to  catch  any  mercury  which  may 
be  spilled.  A  small  measuring-tube  is  provided  to  transfer 
the  mercury  to  the  eudiometer.  This  tube  consists  of  a 
short  piece  of  glass  tubing  closed  at  one  end,  the  open  end 
having  ground  edges.  This  tube  should  be  provided  with  a 
wooden  handle.  The  measuring-tube  is  filled  with  mercury, 
care  being  taken  to  avoid  air-bubbles.  When  the  measur- 
ing-tube is  full  it  is  closed  by  a  ground-glass  plate  and  the 
superfluous  mercury  is  squeezed  out. 

This  measure  of  mercury  is  then  transferred  to  the  eudi- 
ometer, pouring  iu  down  a  funnel  which  should  have  a  long 
glass  tube  attached  to  it  by  india-rubber  tubing.  The 
position  of  the  top  of  the  mercury  meniscus  is  then  read  off 
by  means  of  a  reading-telescope. 


VOLUME  AND  DENSITY. 


19 


Successive  measures  of  mercury  are  added,  care  being 
taken  always  to  read  the  meniscus  after  each  addition  and 
to  avoid  air-bubbles.  Such  a  eudiometer  is  supposed  to  be 
read  by  means  of  a  telescope,  and  to  have  mercury  as  the 
measuring  fluid.  From  the  data  obtained  in  the  calibration 
we  can  construct  a  table  of  relative  capacities  which  is 
sufficient  for  most  purposes:  However,  if  it  is  desired  to 
convert  these  into  absolute  values,  the  capacity  of  the  meas- 
uring-tube must  be  found.  To  determine  this  the  vessel 
should  be  filled  and  its  contents  weighed. 

Calling  W  the  weight  of  the  mercury  and  t  its  tempera- 
ture, the  volume  V  of  the  tube  in  cubic  centimetres  will  be; 
Tf(l  +  0.0001815Q 
13.596"       ' 

where  13.596  is  the  density  and  0.0001815  the  coefficient  of 
cubical  expansion  of  mercury. 


6 

— a 


FIG.  9. 

Before  constructing  a  table  it  is  well  to  notice  that  the 
mercury  meniscus  during  calibration  is  turned  the  opposite 
way  from  the  position  it  would  occupy  when  in  actual  use. 
The  space  occupied  by  the  gas  will  hence  be  greater  than  its 
calibration  value  by  twice  the  space  between  the  convex 
meniscus  and  its  tangent  plane  (Fig.  9). 


20  MEASUREMENTS. 

The  value  of  this  space  can  be  determined  as  follows: 
First  read  the  height  of  the  meniscus  in  the  usual  manner, 
and  then  pour  upon  the  surface  of  the  mercury  a  few  drops 
of  mercuric  chloride  solution,  when  the  surface  will  at  once 
become  horizontal.  The  height  can  now  be  read  again,  and 
the  difference  between  the  two  readings  will  give  the  value 
of  the  space  between  the  meniscus  and  the  tangent  plane. 
By  doubling  this  we  obtain  the  desired  correction,  which 
must  be  added  to  the  calibration  values  in  order  to  record 
the  correct  volume  of  the  gas  when  the  instrument  is  used 
in  the  inverted  position. 

Density  (Specific  Gravity). — The  density  of  a  body  is  the 
mass  of  unit  volume. 

For  solids  and  liquids  the  mass  of  one  cubic  centimetre  of 
water  at  4°  C.  is  taken  as  the  unit  of  mass.  From  this  we 
may  then  define  the  density  of  a  body  as  the  ratio  of  its 
mass  to  the  mass  of  an  equal  volume  of  water  at  4°  C.  The 
specific  gravity  of  a  body  is  the  weight  of  unit  volume. 
Since  in  a  vacuum  the  ratio  of  the  masses  of  bodies  and  the 
ratio  of  their  weights  are  identical,  both  are  expressed  by 
the  same  numerical  value.  For  gases,  dry  air  is  usually 
taken  as  the  standard  of  reference.  The  vapor  density  of  a 
gas  is  then  the  ratio  of  the  mass  of  unit  volume  of  the  gas  to 
the  mass  of  an  equal  volume  of  dry  air  under  similar  condi- 
tions of  temperature  and  pressure. 

The  reciprocal  of  the  specific  gravity  is  known  as  the 
specific  volume,  while  the  volumes  occupied  by  the  weights 
corresponding  to  the  atomic  and  molecular  weights  are 
called  the  atomic  and  molecular  volumes. 

i.  Density  of  Solids. — Of  the  many  methods  for  deter- 
mining the  density  of  a  solid  the  pyknometric  method  is 
the  one  most  frequently  employed  in  the  physico-chemical 
laboratory.  Numerous  forms  of  this  instrument  have  been 


VOLUME  AND  DENSITY. 


21 


devised,  but  the  simple  form  here  shown  (Fig.  10)  is  as 
satisfactory  as  any  for  determining  the  density  of  a  solid.  It 
consists  of  a  glass  bottle  (having  a  capacity  of  50  c.c.)  pro- 
vided with  an  accurately  ground  glass  stopper.  Through 
this  stopper  there  passes  a  fine  hole,  through  which  the 
excess  of  liquid  escapes  when  the  stopper  is  inserted. 


FIG.  10. 

The  use  of  the  pyknometer  involves  three  weighings:  (1) 
pyknometer  filled  with  air;  (2)  pyknometer  filled  with 
water;  and  (3)  pyknometer  filled  with  water  and  the  sub- 
stance of  which  the  density  is  sought.  Let  the  weight  of 
the  substance  be  denoted  by  ws,  the  weight  of  water  required 
to  fill  the  pyknometer  at  temperature  t  by  wa,  and  the  weight 
of  the  substance  and  water  in  pyknometer  by  w&;  then  the 
specific  gravity  without  corrections  will  be 


Reducing  this  to  vacuum  and  to  the  temperature  4°  C.,  we 
have 


w, 


ws+wa-wb^ 

where  Q  denotes  the  specific  gravity  of  the  water  at  tem- 
perature t  and  ^  =  0.0012,  the  mean  density  of  air  in  reference 
to  water  at  4°  C. 


22  MEASUREMENTS. 

If  the  temperature  at  the  time  of  weighing  the  water  is 
different  from  that  at  the  time  of  weighing  the  water  and 
substance,  a  correction  must  be  introduced  for  the  expan- 
sion of  both  water  and  glass.  The  above  formula  then  takes 
the  form 

s=  __  "•«?  -V  ,  j 

-  wb+wJ[Q  -Qa+3p(t  -to)] 


where  t  and  Q  represent  the  temperature  and  specific  gravity 
of  water  at  the  time  of  weighing  the  water  and  substance, 
ta  and  Qa  the  corresponding  values  at  the  time  of  weighing  the 
water  alone,  and  3/2  the  coefficient  of  cubical  expansion  of 
glass  =  0.000025. 

Should  the  substance  of  which  the  specific  gravity  is 
sought  be  soluble  in  water,  other  liquids  may  be  used  in  its 
place,  in  which  case  the  above  formula  must  be  multiplied 
by  the  specific  gravity  of  the  liquid  substituted. 

The  method  of  procedure  in  determining  the  specific 
gravity  of  a  solid  with  the  pyknometer  is  as  follows:  The 
pyknometer  is  thoroughly  cleaned,  then  dried  with  alco- 
hol and  ether,  and  then  weighed.  It  is  then  filled  with 
distilled  water,  care  being  taken  to  insure  the  absence  of 
air-bubbles.  The  excess  of  water  which  exudes  when  the 
stopper  is  inserted  is  removed  with  filter-paper,  and  the 
pyknometer  is  weighed  again.  From  these  two  weighings 
the  weight  of  the  water  wa  is  calculated.  Finally  the  sub- 
stance is  weighed  either  inside  or  outside  the  pyknometer, 
and  its  weight  gives  us  ws. 

By  weighing  the  pyknometer  containing  the  substance 
and  filled  with  water  we  obtain  Wb-  From  these  data  we 
may  calculate  the  uncorrected  specific  gravity.  To  obtain 
the  exact  specific  gravity  it  will  be  evident,  from  what  has 
been  said,  that  due  regard  must  be  paid  to  the  temperature. 
Should  it  be  required  to  determine  the  specific  gravity  of 


VOLUME  AND  DENSITY. 


23 


substances  which  are  too  light,  they  may  be  made  to  sink 
by  placing  in  a  vessel  of  glass  or  in  a  wire  cage,  which  remains 
in  the  pyknometer  during  all  the  weighings. 

It  is  obvious  that  the  pyknometer  should  not  be  grasped 
by  the  hands.  The  finer  the  state  of  aggregation  of  the 
solid  the  greater  the  error  in  the  determination  of  its  spe- 
cific gravity.  This  is  due  largely  to  inclosed  air  or  to  adher- 
ing impurities. 

2.  Density  of  Liquids. — (a)  The  Pyknometer. — While  the 
pyknometer  just  described  may  be  used  for  the  determination 
of  the  specific  gravity  of  a  liquid,  yet  another  form,  known 
as  the  Sprengel-Ostwald  pyknometer  (Fig.  11),  is  given 


FIG.  11. 

preference  in  most  laboratories.  With  an  instrument  hold- 
ing 25  c.c.  determinations  may  be  made  with  a  probable 
error  of  about  ±0.00002. 

The  pyknometer  is  weighed  (1)  filled  with  air,  (2)  with 
water,  and  (3)  with  liquid  of  which  the  density  is  sought. 
The  apparent  weight  of  the  liquid  in  air  is  denoted  by  wa, 
and  the  weight  of  an  equal  volume  of  water  by  wa.  The 

uncorrected  specific  gravity  is  then  — .     Reduced  to  water  at 

wa 

4°  C.  and  to  vacuum,  we  have 


24 


MEASUREMENTS. 


If  the  specific  gravity  of  the  liquid  is  determined  at  a  tem- 
perature different  from  that  at  which  the  water  is  deter- 
mined, the  specific  gravity  is  calculated  from  the  following 
formula  : 


W 

where  the  additional  symbols  have  the  signification  of  the 
previous  paragraph. 

The  usual  size  of  the  pyknometer  is  from  5  to  20  c.c. 
capacity,  the  larger  sizes  being  selected  for  the  most  accu- 
rate determinations. 

To  carry  out  a  determination  of  specific  gravity  with  the 
Sprengel-Ostwald  pyknometer,  it  is  first  cleaned,  then  dried 
with  alcohol  and  ether,  and  then  carefully  weighed.  It 
is  then  filled  with  the  liquid  under  investigation  either  by 
means  of  the  mouth  or  an  aspirator,  as  shown  in  Fig.  12, 


FIG.  12. 

care  being  taken  to  avoid  the  introduction  of  air-bubbles. 
When  completely  filled  the  pyknometer  is  hung  in  a  con- 
stant-temperature bath,  so  that  only  the  upper  tubes  are 
out  of  water.  If  the  determination  is  to  be  made  accurate 
to  the  fourth  decimal  place,  the  temperature  of  the  bath 
must  remain  constant  to  within  0.2°.  The  quantity  of 
liquid  in  the  pyknometer  is  regulated  so  that  the  smaller 
tube  remains  completely  filled,  while  the  liquid  in  the  other 


VOLUME  AND  DENSITY.  25 

tube  remains  at  the  mark.  This  adjustment  can  be  effected 
by  the  careful  use  of  a  bit  of  filter-paper  and  a  glass  rod 
with  a  drop  of  the  liquid  upon  it.  When  the  quantity  of 
the  liquid  is  properly  adjusted  the  tubes  are  carefully  wiped 
with  filter-paper  and  a  handkerchief  and  small  glass  caps 
put  on.  The  whole  apparatus  is  then  dried,  great  care 
being  taken  that  the  heat  of  the  hand  does  not  reach  the 
tubes.  The  pyknometer  is  then  hung  on  the  arm  of  the 
balance  and  weighed. 

The  same  procedure  is  followed  in  weighing  the  pyk- 
nometer filled  with  water. 

In  this  case,  as  in  all  density  determinations,  the  water 
used  should  be  air-free  distilled  water.  For  rapid  deter- 
minations of  the  specific  gravity  of  a  liquid  use  may  be  made 
of  a  1-c.c.  pipette  (Fig.  13)  with  tubes  of  almost  capillary 


FIG.  13. 

dimensions.  It  is  filled  by  sucking  the  liquid  up  to  a  mark 
on  the  stem,  and  can  be  placed  on  the  pan  of  the  balance  by 
means  of  a  light,  bent  wire  frame. 

With  this  rough  apparatus  results  accurate  to  the  thou- 
sandths place  of  decimals  may  be  obtained. 

(6)  The  Mohr-Westphal  Balance. — When  it  is  desired  to 
obtain  only  an  approximation  to  the  true  density  of  a  liquid 
this  instrument  is  of  great  value,  since  the  results  can  be 
secured  in  a  very  short  time.  The  accompanying  figure 
(Fig.  14)  shows  the  instrument  in  its  most  common  form. 
The  beam  ABC  is  pivoted  at  B,  the  longer  arm  EC  having 
nine  equally  spaced  notches  at  which  riders  may  be 
placed.  From  the  hook  at  (7  there  hangs  by  a  small 
platinum  wire  a  float,  F,  while  at  the  end  A  there  is  a 


26 


ME  AS  UREMENTS. 


weight  which  serves  as  a  counterbalance.  The  balance  has 
been  so  adjusted  that  when  the  float  hangs  from  the  arm 
the  beam  should  be  in  equilibrium,  which  is  indicated  by 
the  points  at  a  being  opposite  each  other.  If  it  is  found 
that  the  points  do  not  come  opposite  each  other,  the 
requisite  adjustment  may  be  made  by  means  of  the  levelling- 


FIG.  14. 

screw  s.  When  the  float  is  in  water  at  15°  C.,  equilibrium  is 
restored  by  placing  one  of  the  four  riders  (call  it  A)  on  the 
hook,  this  position  being  the  tenth  division  of  the  arm. 

The  remaining  three  riders  are  B  =  A,  <?  =  77     and  D  = 


If  it  is  required  to  find  the  density  of  a  liquid  lighter  than 
water,  it  is  only  necessary  to  place  the  liquid  in  the  glass 
cylinder  and  allow  the  float  to  be  immersed  in  it,  and  then 
to  add  riders  to  the  beam  until  equilibrium  is  secured.  Sup- 
pose B  to  be  at  7,  C  at  4,  and  D  at  8,  then  the  density  of  the 
liquid  is  0.748. 


VOLUME  AND  DENSITY.  27 

On  the  other  hand,  should  the  liquid  be  heavier  than 
water,  the  rider  A  is  first  hung  from  the  hook  at  the  end  of 
the  beam.  Let  us  suppose  that  the  other  riders  have  the 
following  positions:  B  at  6,  C  at  2,  and  D  at  6.  Then  the 
density  of  the  liquid  is  1.626. 

The  adjustments  in  air  and  in  water  must  never  be 
omitted.  If  the  adjustment  for  water  is  not  exact  when  A 
is  hung  from  the  hook,  the  final  adjustment  must  be  secured 
with  the  other  riders  and  the  corresponding  correction  ap- 
plied to  the  results.  This  correction  can  be  obtained  by 
dividing  the  final  reading  by  the  weight  on  the  beam;  thus 
if  the  weight  on  the  beam  be  0.996  instead  of  1,  the  final 
reading  must  be  divided  by  0.996. 

Care  must  be  taken  to  protect  the  knife-edges  from  rust, 
since  the  sensibility  would  be  seriously  impaired.  By  in- 
creasing the  size  of  the  divisions  of  the  beam  and  taking 
greater  care  in  the  construction  of  the  weights  it  is  possible 
to  obtain  results  of  much  greater  accuracy.  Kohlrausch 
and  Hallwachs  claim  to  be  able  to  determine  density  to  the 
sixth  place  of  decimals  by  means  of  the  hydrostatic  prin- 
ciple. 

Density  of  Gases  (Vapor  Density). — The  determination 
of  vapor  density  is  one  of  the  frequent  operations  of  the 
physico-chemical  laboratory. 

The  methods  in  use  for  the  measurement  of  vapor  density 
are: 

(1)  The  method  of  Dumas. 

(2)  The  method  of  Gay-Lussac. 

(3)  The  method  of  Hofmann. 

(4)  The  method  of  Victor  Meyer. 

(5)  The  method  of  Bunsen. 

The  general  principles  of  all  these  methods  are  well  known 
to  both  the  student  of  chemistry  and  the  student  of  physics. 


28  MEASUREMENTS. 

Of  these  five  methods  but  two  will  be  treated  here,  the 
method  of  Dumas,  involving  the  determination  of  the  mass 
of  a  definite  volume  of  substance,  and  the  method  of  Victor 
Meyer,  depending  upon  the  dete  mination  of  the  volume  of 
a  given  mass  of  substance.  With  both  of  these  methods 
the  volume  of  gas  is  reduced  to  standard  temperature,  and 
pressure  through  the  application  of  the  laws  of  Boyle  and 
Charles. 

Method  of  Dumas. — The  apparatus  required  for  this 
method  is  extremely  simple.  It  consists  of  a  thin-walled 
glass  balloon  of  100  to  300  cc.  capacity,  having  a  narrow  neck, 
as  shown  in  Fig.  15.  There  is  also  required  a  water,  oil 


FIG.  IB. 

or  paraffine  bath  provided  with  a  device  for  keeping  the 
balloon  immersed  in  the  liquid.  To  determine  the  vapor 
density  of  a  liquid  by  means  of  this  apparatus  the  balloon 
is  first  weighed  full  of  air,  precautions  being  taken  to  insure 
the  absence  of  moisture  from  the  inner  and  outer  walls. 

The  balloon  is  then  gently  heated  and  the  neck  is  dipped 
below  the  surface  of  the  liqu  d  under  examination,  the  flame 
is  removed  and  several  grams  of  liquid  are  allowed  to  enter. 

The  balloon  is  then  placed  in  +he  heat'ng  bath,  Fig.  16, 
up  to  the  contracted  portion  A.  The  temperature  of  the 
bath  is  adjusted  so  that  it  is  about  10°  above  the  boiling 
point  of  the  liquid  under  nvestigation.  When  the  liquid 
has  become  completely  vaporized  and  the  air  in  the  balloon 


VOLUME  AND  DENSITY. 


29 


has  been  entirely  driven  out,  the  neck  is  sealed  off  at  A  by 
means  of  the  blowpipe.  The  balloon  is  then  removed  from 
the  bath  and  is  allowed  to  acquire  room  temperature.  As 


FIG.  16. 

soon  as  the  balloon  is  removed  from  the  bath  the  tempera- 
ture of  the  bath  is  taken  and  the  height  of  the  barometer 
is  also  observed. 

When  the  balloon  has  cooled  to  the  temperature  of  the 
room  it  is  weighed  together  with  the  piece  of  tubing  which 
was  sealed  off.  The  barometric  reading  is  again  taken  and 
also  the  temperature  of  the  balance  case  is  noted.  The  neck 
of  the  balloon  is  now  dipped  under  the  surface  of  some 
freshly  boiled  distilled  water  and  the  point  is  broken  off. 
If  the  balloon  fills  completely  with  water  we  know  that  the 
air  has  been  entirely  displaced  by  the  vapor  of  the  sub- 
stance, otherwise  not. 

If  the  filling  be  complete,  the  balloon  filled  with  water, 
and  the  melted-off  piece  of  tubing  is  placed  upon  the  balance 
and  weighed  to  within  one  centigram.  It  is  a  frequent 
occurrence,  however,  that  the  vapor  does  not  entirely  expel 
the  air,  under  which  circumstances  the  water  does  not  fill 
the  balloon  completely  when  the  stem  is  broken.  If  this 


30  MEASUREMENTS. 

should  occur  the  balloon  is  immersed  until  the  water  stands 
at  the  same  level  inside  and  out.  The  balloon  is  then  weighed 
with  this  quantity  of  water;  it  is  then  filled  completely 
with  water  and  reweighed.  From  the  data  thus  obtained 
it  is  possible  to  calculate  the  vapor  density  by  means  of  the 
formula, 


where  the  symbols  have  the  following  significance: 
m  =  the  weight  of  the  empty  balloon; 
w'  =  the  weight  of  the  balloon  filled  with  vapor; 
-M"=the  weight  of  the  balloon  completely  filled  with  water; 
M'  =  the  weight  of  the  balloon  partially  filled  with  water; 
£  =  the  temperature  of  the  bath  at  the  time  of  sealing; 
6  =  the  barometric  reading  at  the  time  of  sealing; 
£'  =  the  temperature  of  balloon  filled  with  vapor  at  the  time 

of  weighing; 
b'  =  the   barometric   reading  at  time  of   weighing   balloon 

filled  with  vapor; 
A  =  the  density  of  the  air  at  the  time  of  weighing  balloon 

filled  with  vapor; 

3/?=the  cubical  expansion  of  glass  or  0.000025; 
Q  =  the  density  of  the  water  used  in  filling  the  balloon. 

For  the  derivation  of  this  formula  the  student  is  referred 
to  the  "Leitfaden  der  praktischen  Physik,"  by  Kohlrausch, 
page  69. 

Method  of  Victor  Meyer  (Air  Displacement).  —  A  cylin- 
drical glass  vessel,  A  (Fig.  17),  is  furnished  at  the  top  with  a 
longer  tube,  a.  This  vessel  is  placed  in  an  outer  glass  tube, 
B,  in  which  some  substance  is  heated  to  boiling  in  order  to 


VOLUME  AND  DENSITY.  31 

maintain  A  at  constant  temperature.  When  substances  of 
high  boiling-points  are  used  it  is  better  to  employ  a  vessel 
of  copper  for  B.  The  tube  A  is  closed  with  a  rubber  stop- 
per, and  by  means  of  a  side  tube  is  connected  with  the  eudi- 
ometer, e,  which  is  filled  with  freshly  boiled  water.  The  air 
displaced  by  the  vaporization  of  the  substance  in  A  is  col- 
lected in  e  and  its  volume  measured.  The  substance  is 
weighed  in  a  small  thin-walled  flask  or  weighing-tube,  and  is 
introduced  into  the  tube  A  by  means  of  the  device  shown 
in  the  illustration  at  c.  The  weighing-tube  is  placed  upon 
the  glass  rod  which  is  introduced  into  the  side  tube,  and  the 
entrance  to  the  vaporizing  vessel  closed  by  means  of  an  elas- 
tic-rubber tube  which  allows  the  glass  rod  to  pass  in  or  out 
freely.  When  the  required  temperature  is  reached  the 
weighing-tube  is  dropped  from  the  glass  rod  into*  the  heated 
tube  A,  the  bottom  of  which  is  cushioned  with  asbestos  or 
glass  wool. 

Carrying  out  a  Determination. — The  vaporizing-tube  is 
washed,  dried  with  alcohol  and  ether,  and  the  apparatus 
then  assembled.  A  heating  substance  is  chosen  with  a 
melting-  or  boiling-point  30-40°  C.  higher  than  the  boiling- 
point  of  the  substance  under  investigation.  Among  heating 
substances  commonly  in  use  may  be  mentioned:  water, 
100°;  aniline,  183°;  nitrobenzene,  211°;  diphenylamine, 
300°;  paraffin,  350°;  sulphur,  400°.  When  the  apparatus 
is  all  set  up  the  jacket  is  heated  carefully,  and  as  soon  as 
air-bubbles  cease  rising  in  the  liquid,  which  serves  as  the 
outlet  to  the  vaporizing-tube,  the  weighing-tube  is  intro- 
duced and  supported  at  c.  After  the  temperature  of  the 
vapor-chamber  has  become  constant  and  the  measuring- 
cylinder  e,  filled  with  water,  remains  free  from  air  for  some 
time,  the  weighing-tube  is  dropped  into  A  by  pulling  out 
the  glass  rod  at  c. 


32 


MEASUREMENTS. 


J  V 


/  \ 


PIG.  17. 


VOLUME  AND  DENSITY.  33 

Immediately  air-bubbles  begin  to  rise  in  e,  each  molecule 
of  displaced  air  corresponding  to  one  molecule  of  the  vapor- 
izing substance.  When  no  more  air  passes  into  e  the  con- 
nection with  the  vaporizing  apparatus  is  broken  and  the 
volume  of  air  is  reduced  to  0°  C.  and  760  mm.  The  volume 
of  air  should  be  at  least  30-40  c.c.  To  produce  this  volume 
of  air  0.1  to  0.2  gram  of  the  substance  is  generally  suffi- 
cient. Instead  of  using  air  as  a  medium  the  vaporizing- 
tube  may  be  filled  with  hydrogen,  nitrogen,  or  carbon  dioxide. 
The  results  of  an  experiment  may  be  calculated  from 
the  data  obtained,  as  follows: 

Let  g  =  weight  of  substance  in  grams; 
v  =  volume  of  displaced  air; 
p  =  pressure  in  millimetres  of  mercury; 
h  =  height  of  water  column  in  measuring-cylinder; 
/==  vapor  tension  of  water  at  £°; 
£  =  temperature  of  enclosed  air; 
b  =  barometric  pressure; 
d  =  vapor  density. 
Then 

g  0X760(1+0.003670 

~~t>0X  0.001293"       vpX  0.001293       ' 
The  value  of  p  is  found  from  the  expression 


The  value  of  /  is  to  be  found  in  the  tables  of  vapor  ten- 
sion. 


CHAPTER  III. 

THERMOSTATS. 

TEMPERATURE  is  one  of  the  most  important  factors 
conditioning  chemical  reactions  and  it  is  absolutely  essential 
to  have  some  means  whereby  constant  temperatures  can  be 
maintained  over  long  periods  of  time.  The  constant  tem- 
perature bath  or  thermostat  hence  deserves  careful  con- 
sideration in  the  equipment  of  the  physico-chemical  labora- 
tory. 

The  method  to  be  employed  obviously  depends  upon  the 
temperature  desired.  The  fact  that  pure  substances  in 
general  melt  and  boil  at  well  defined  temperatures  is  fre- 
quently made  use  of  in  obtaining  constant  temperatures. 
A  mixture  of  pure  ice  and  pure  distilled  water  affords  a  very 
satisfactory  bath  if  a  temperature  of  0°  is  required.  Cryo- 
hydric  and  transition  temperatures  can  also  be  employed 
with  very  satisfactory  results.  A  list  of  hydrates  with  their 
melting  points  is  given  on  page  57.  The  vapors  of  various 
boiling  liquids  can  be  used  with  advantage,  although  the 
temperatures  obtained  are  more  or  less  dependent  upon 
barometric  pressure. 

Thermostats  involving  the  use  of  a  fusing  solid  or  a  boiling 
liquid  are  both  open  to  the  objection  that  the  experimenter 
is  limited  to  certain  fixed  temperatures  which  can  only  be 
varied  by  the  employment  of  complicated  apparatus  for 
increasing  or  diminishing  the  pressure. 

34 


THERMOSTATS.  35 

For  this  reason  by  far  the  greater  number  of  thermostats 
make  use  of  some  liquid  which  is  maintained  at  constant 
temperature  by  means  of  an  automatically  controlled  heater. 
Such,  thermostats  may  be  considered  as  made  up  of  five 
parts:  the  tank,  the  bath,  the  temperature  regulator,  the 
stirrer,  and  the  heater. 

The  Tank. — The  tank  may  be  made  either  or  wood  or 
metal  according  to  the  method  of  heating.  For  most  pur- 
poses tanks  of  galvanized  iron  are  used.  These  are  jacketed 
with  felt  or  asbestos  to  prevent  radiation.  In  the  experience 
of  the  author  asbestos  has  proven  very  satisfactory.  This 
may  be  cemented  to  the  galvanized  iron  by  means  of  a  solu- 
tion of  water  glass,  both  sides  and  bottom  of  the  tank 
being  covered  and  thus  minimizing  radiation.  The  interior  of 
the  tank  should  be  painted,  preferably  with  white  "enamel" 
paint. 

When  electric  heating  is  employed  a  wooden  tank  made 
from  clear  pine  is  highly  satisfactory.  This  should  be 
properly  caulked  with  white  lead.  For  viscosity  and  other 
measurements  where  transparent  sides  are  required,  the 
wooden  tank  with  electric  heating  is  much  superior  to  the 
iron  tank. 

The  Bath. — For  all  ordinary  purposes  water  is  the  most 
widely  used  bath  liquid.  It  can  be  used  up  to  within  a  few 
degrees  of  its  boiling  point,  but  when  temperatures  exceed- 
ing 50°  are  required  it  is  advisable  to  cover  the  surface  of 
the  water  with  a  layer  of  paraffin  oil  to  prevent  evaporation. 
It  is  also  feasible  to  attach  a  constant  level  device  to  the 
tank  when  temperatures  above  50°  are  desired  and  thus 
eliminate  the  necessity  for  the  layer  of  oil  which  at  times  is 
troublesome. 

For  temperatures  above  100°  either  concentrated  solu- 
tions of  various  salts  or  high  boiling  liquids  may  be  used. 


36 


MEASUREMENTS. 


The  Temperature  Regulator. — The  form  of  temperature 
regulator  employed  depends  upon  whether  it  is  to  be  used 
for  temperatures  above  or  below  that  of  the  room.'  For 
experiments  above  room  temperature  probably  the  most 


FIG.  18. 

satisfactory  is  the  toluene  regulator  shown  in  Fig.  18.  The 
bulb  A  is  filled  with  toluene  and  the  stem  and  a  portion  of 
the  bend  contains  mercury. 

The  upper  portion  of  the  stem  is  contracted  to  capillary 
dimensions  in  order  to  increase  the  sensitiveness  of  the 
regulator.  The  gas  enters  through  the  tube  B  which  passes 
tightly  through  a  cork  in  the  enlarged  upper  portion  of  the 


THERMOSTATS.  37 

stem.  The  tube  C  serves  to  lead  the  gas  to  the  burner 
below  the  tank.  Should  the  temperature  of  the  bath  rise 
sufficiently  to  cause  the  mercury  in  the  stem  to  completely 
close  the  mouth  of  the  tube  B,  the  gas  finds  an  exit  through 
a  small  hole  D  in  the  tube  B.  This  insures  the  flame  at  the 
burner  from  being  extinguished  and  yet  leaves  a  flame  so 
small  as  to  be  practically  ineffective  in  heating  the  water 
in  the  tank. 

As  the  temperature  of  the  bath  falls  the  mercury  in 
the  regulator  contracts,  the  flow  of  gas  increases  once  more 
and  the  desired  temperature  is  again  restored.  When  the 
regulator  is  properly  adjusted  the  variation  in  temperature 
should  not  exceed  0.1°. 

The  process  of  filling  the  toluene  regulator  calls  for  a  word 
of  direction.  To  fill  the  regulator  the  inlet  tube  B  is  re- 
moved and  the  upper  end  of  the  stem  is  closed  with  a  tight- 
fitting  cork  which  is  free  from  defects.  To  the  end  of  the 
tube  C  is  attached  a  rubber  tube  leading  to  a  glass  tube 
fitted  with  a  three-way  stop-cock,  which  is  in  turn  connected 
with  the  water-pump.  The  stop-cock  is  so  turned  that  com- 
munication is  established  with  the  water  pump  and  the  regu- 
lator is  exhausted  as  completely  as  possible.  When  this 
has  been  accomplished  the  free  end  of  the  tube  carrying  the 
stop-cock  is  placed  in  a  vessel  of  toluene  and  the  stop-cock 
is  turned  so  as  to  allow  the  toluene  to  rush  into  the  exhausted 
regulator.  After  as  much  toluene  has  entered  the  regulator 
as  will  enter,  the  stop-cock  is  again  turned  to  its  original 
position  and  the  pump  is  started  once  more.  To  aid  in 
the  removal  of  the  air  the  bulb  of  the  regulator  is  immersed 
in  boiling  water  and  the  exhaustion  is  continued  until  the 
toluene  boils  and  the  stem  is  filled  with  the  vapor.  The 
stop-cock  is  now  turned  again  and  more  toluene  is  allowed 
to  enter. 


38  MEASUREMENTS. 

This  process  is  repeated  until  the  regulator  is  nearly  filled 
with  toluene.  The  cork  is  now  removed,  a  quantity  of  mer- 
cury is  poured  in,  the  cork  is  replaced,  and  after  giving  the 
tube  an  inclination  so  that  the  mercury  does  not  choke  the 
capillary,  the  regulator  is  once  more  exhausted.  The  tube 
is  now  placed  in  an  upright  position  and  air  is  admitted. 

This  operation  has  to  be  repeated  until  the  regulator 
contains  sufficient  mercury.  The  amount  of  mercury  to 
be  used  depends  upon  the  temperature  for  which  the 
regulator  is  to  be  adjusted.  For  ordinary  purposes  the 
mercury  should  form  a  layer  about  1  cm.  deep  in  the  wide 
part  of  the  stem. 

A  little  toluene  is  likely  to  remain  on  the  surface  of  the 
mercury  after  the  filling  of  the  regulator,  and  this  is  removed 
by  means  of  a  piece  of  filter-paper. 

When  the  regulator  has  been  filled  as  directed  the  final 
adjustment  is  effected  by  placing  the  regulator  in  a  bath 
having  the  desired  temperature  and  allowing  it  to  remain 
there  until  the  mercury  comes  to  rest.  If  there  be  an  excess 
of  mercury  it  is  removed  by  means  of  a  pipette  until  the 
mercury  meniscus  stands  just  above  the  lower  end  of  the 
enlarged  portion  of  the  stem.  If  there  be  a  deficiency  of 
mercury  the  regulator  is  placed  in  a  beaker  of  hot  water, 
and  when  the  mercury  has  risen  in  the  capillary  tube  more 
is  added  from  the  pipette.  The  regulator  is  then  returned 
to  the  bath  and  the  level  of  the  meniscus  adjusted  as  above. 
The  exact  adjustment  is  accomplished  by  moving  the  tube 
B  either  up  or  down. 

For  temperatures  below  that  of  the  room  the  most  satis- 
factory form  is  that  due  to  Foote,  shown  in  Fig.  19. 

This  is  filled  with  toluene,  as  in  the  case  of  the  regulator 
just  described.  The  level  of  the  mercury  is  adjusted  by 
means  of  the  side-screw  e.  Ice-cold  water  is  led  in  through 


THERMOSTATS 


39 


a  and  flows  out  through  the  side  tube  b  into  the  bath.  As 
the  temperature  of  the  bath  falls  the  mercury  in  the  regulator 
contracts  and  the  mouth  of  the  exit  tube  c  is  opened  and  the 
ice-cold  water  is  then  discharged  into  the  waste-pipe.  If 
precautions  are  taken  to  insure  the  rate  of  inflow  being 


xu 

FIG.  19. 

slightly  less  than  the  rate  at  which  c  can  discharge  the  waste 
water,  the  regulator  gives  perfect  satisfaction. 

Where  large  tanks  are  used  the  Ostwald  gas-regulator  is, 
perhaps,  more  satisfactory  than  the  toluene,  owing  to  the 
increased  dimensions  of  the  bulb.  An  account  of  this 
regulator  will  be  found  in  the  chapter  on  Solubility. 


40 


MEASUREMENTS. 


Stirrers.— To  insure  uniform  temperature  throughout  the 
bath  it  is  quite  essential  that  it  should  be  slowly  agitated. 
To  accomplish  this  various  devices  have  been  employed, 
but  perhaps  the  most  satisfactory  is  a  simple  three-  or  four- 
bladed  paddle-wheel  which  is  turned  by  means  of  a  hot- 
air  engine,  an  electric  motor  or  a  water  turbine.  In  cases 
where  there  is  little  room  for  a  stirrer  the  forms  shown  in 
Fig.  110  will  be  found  efficient. 

The  Heater. — The  source  of  heat  may  be  either  a  Bunsen 
burner  or  a  coil  heated  by  means  of  an  electric  current. 


FIG.  20. 

When  a  Bunsen  burner  is  used  it  is  convenient  to  have  a 
burner  with  a  chimney  to  prevent  the  flame  being  blown 
aside  by  air  currents.  Apparatus  makers  furnish  a  burner 
specially  adapted  to  heating  thermostats.  It  is  fitted  with 
a  steatite  tip  and  a  screw-adjustment  of  the  gas  supply. 

A  very  satisfactory  form  of  thermostat  is  shown  in  Fig.  20. 


THERMOSTATS.  41 

The  wooden  tank  TT  is  provided  with  an  electric  heating 
coil  H. 

The  heating  circuit  may  be  broken  at  G  by  means  of  the 
armature  of  the  electro-magnet  M,  which  is  controlled  by 
the  toluene  regulator  in  the  tank.  Let  us  suppose  that  the 
water  in  the  tank  is  below  the  desired  temperature  and  the 
current  through  the  heating  circuit  is  closed.  The  stirrer 
K  serves  to  keep  the  temperature  of  the  bath  homogeneous 
and  the  gradually  rising  temperature  of  the  water  causes 
the  mercury  in  the  stem  of  the  regulator  to  rise.  At  0 
there  is  fused  into  the  stem  of  the  regulator  a  platinum  wire 
which  is  connected  with  the  battery  J  through  the  electro- 
magnet M. 

Through  the  cork  D  at  the  top  of  the  regulator  a  stout 
platinum  wire  is  passed,  the  position  of  the  end  of  the  wire 
B  being  determined  by  the  temperature  it  is  desired  to 
maintain  in  the  bath.  When  the  l>ath  has  reached  the  re- 
quired temperature  the  mercury  hi  the  stem  makes  contact  at 
B  with  the  platinum  wire  which  is  in  turn  connected  with 
the  battery  J. 

The  current  through  the  electro-magnet  is  closed,  the 
armature  is  drawn  down  and  the  heating  circuit  is  broken. 

When  the  bath  begins  to  cool  the  mercury  in  the  regulator 
falls,  the  electro-magnet  circuit  is  broken  at  B  and  the 
heating  circuit  is  again  closed  through  the  armature  which 
is  brought  in  contact  with  G  by  means  of  the  spring  7. 

This  device  has  many  advantages  over  those  in  which  gas 
is  employed  as  the  source  of  heat. 


CHAPTER  IV, 

VISCOSITY  AND  SURFACE  TENSION. 

VISCOSITY,  or  fluid  friction,  may  be  explained  by  the 
accompanying  figure  (Fig.  21).  Let  AB  be  a  horizontal 
plate  over  which  a  liquid  flows  in  the  direction  of  the  arrow. 
The  layer  of  liquid  in  immediate  contact  with  the  surface 
remains  at  rest  on  account  of  adhesion,  and  the  velocity  of 
the  different  layers  increases  as  the  distance  from  the  sur- 


FIG.  21. 

face  increases.  Thus  we  have  a  succession  of  layers  of 
liquid  each  moving  with  a  different  velocity,  the  more 
slowly  moving  layer  tending  to  retard  the  motion  of  the 
adjacent  rapidly  moving  layer.  Thus  any  horizontal  layer 
is  acted  upon  above  by  a  tangential  force  in  the  direction  of 
the  motion  of  the  liquid,  and  below  by  a  second  tangential 
force  in  the  opposite  direction.  These  two  forces  are  what 
is  known  as  viscosity,  or  fluid  friction. 

Flow  of  Fluid  through  a  Long  Tube. — Let  I  be  the  length 
of  the  tube  and  p  its  radius,  p  the  pressure  forcing  the  liquid 
through  the  tube,  and  v  the  velocity  at  a  distance  r  from  the 

42 


VISCOSITY  AND  SURFACE  TENSION.  43 

axis  of  the  tube.  Let  us  imagine  a  cylindrical  portion  of  the 
fluid  of  radius  r  having  the  same  axis  as  the  tube.  The  surface 
of  this  cylindrical  portion  will  move  through  the  tube  with  a 
velocity  v  behaving  like  a  solid  rod.  In  like  manner  the 
cylindrical  surface  of  radius  r+Jr  will  move  through  the 
tube  with  a  velocity  v-\-4v  behaving  like  a  hollow  shell. 
Now  the  fluid  layer  between  the  "  rod  "  and  "  shell"  is  sub- 
jec  Led  to  just  such  conditions  as  any  fluid  layer  between 
thi  plate  and  the  surface  of  the  liquid  in  Fig.  16.  It  has  been 
found  by  experiment  that  the  tangential  force  required  to 
maintain  a  constant  difference  in  velocity  between  two  adja- 
cent layers  of  liquid  moving  in  parallel  directions  varies 
directly  with  the  difference  in  velocity  v  and  inversely 
with  the  distance  x  between  the  layers.  That  is, 


or 

F-l'lJ-J      ....;:.     (1) 

where  r)  is  a  proportionality  factor  known  as  the  coefficient  of 
viscosity. 

Equation  (1)  may  now  be  written 

dv 
F=^,      .......    (2) 

since  Av  corresponds  to  v}  and  Ar  to  x. 

This  stress  being  tangential  over  the  whole  surface  of 

the   rod.    the    resistance   becomes   IxrlF,    or   2xrh—      The 

dv' 

force  which  overcomes  this  resistance  is  nr2p.     The  condi- 
tion of  equilibrium  is  then 

7  dv 
^P  =  ^rlr]—}       .     .     .     .     .     .     (3) 


44 
or 


MEASUREMENTS. 


dv       p 


/dv     pr* 
df=4h 


When  r  =  pj 


Therefore 


and    K=  — 


4 


P 


(4) 


From  this  we  see  that  the  velocity  at  each  part  of  the  tube 
is  determined.  To  find  the  volume  V  of  fluid  which  will 
flow  through  the  tube  in  the  time  t,  consider  the  cross-section 


FIG.  22. 

of  the  tube.  The  area  of  the  section  of  radius  r-f  dr  (Fig.  22) 
is  7r(r2+2rJr+  Jr2),  and  the  area  of  the  section  of  radius  r 
is  ?rr2,  from  which  we  see  that  the  area  of  the  annulus  is 
2nrAr.  The  velocity  over  this  annular  area  is  v.  So  that 
the  volume  of  liquid  AV  flowing  across  this  area  in  time  t  is 


VISCOSITY  AND  SURFACE  TENSION.  45 

-v-t.      Substituting  in  this  expression  the  value 
of  v  in  equation  (4),  we  have 


or 

F-^.    :::::!!!!!   (5) 

From  this  equation  (5)  it  is  possible  to  calculate  the  coeffi- 
cient of  viscosity  T)  when  the  values  of  V,  p,  t,  I,  and  p  have 
been  determined  experimentally. 

Solving  equation  (5)  for  13,  we  obtain 


. 
•     5     5     C     C     5     •     \W 

The  factor  ij  may  now  be  defined  as  the  work  necessary  to 
move,  hi  unit  time,  two  layers  of  liquid  surface  in  parallel 
but  opposite  directions;  the  distance  moved  being  equal  to 
the  distance  between  the  layers.  If  the  liquid  issues  from 
the  tube  with  a  finite  velocity,  the  coefficient  must  be  dimin- 

sV 

ished  by  -5  —  ,  where  g  is  the  acceleration  due  to  gravity,  or 
ring 

981,  and  s  the  specific  gravity  of  the  liquid.  The  constant 
R  according  to  Hagenbach  is  10.08,  while  Wilberforce  and 
Finkener  assign  8  as  the  more  probable  value.  Since  for  the 
same  apparatus  all  the  factors  entering  into  the  expression 
for  the  coefficient  of  viscosity  are  constant  with  the  excep- 
tion of  the  specific  gravity  and  the  time,  the  corrected  for- 
mula may  be  written 


46  MEASUREMENTS. 

The  values  of  the  constants  K  and  Kl  are  to  be  determined 
for  each  apparatus.  The  apparatus  is  so  designed  that  the 

K  s 
value  of  —  j-  is  extremely  small  in  comparison  with  the  value 

t 

Of  7?. 

Frequently,  instead  of  determining  y,  the  specific  viscosity 
is  determined  instead. 

By  the  term  specific  viscosity  is  understood  the  time  of 
outflow  of  the  liquid  at  any  one  temperature  divided  by  the 
time  of  outflow  for  water  at  0°  C.  It  is  customary  to  intro- 
duce the  arbitrary  factor  100,  so  that  the  specific  viscosity  Q 
is  determined  by  the  expression 


(7) 


Measurement  of  the   Coefficient    of    Viscosity.  —  (a)  Poi- 

seuille-Ostwald.  —  The  method  here  given  for  the  measure- 
ment of  this  quantity  was  originally  devised  by  Poiseuille, 
and  later  improved  by  Ostwald.  The  apparatus  required 
for  the  determination  of  the  coefficient  of  viscosity  is  shown 
in  Fig.  23. 

The  liquid  is  allowed  to  flow  under  its  own  pressure 
through  the  capillary  bd.  An  accurately  known  quantity  of 
the  liquid  is  introduced  at  /,  and  by  applying  suction  at  a  it 
is  drawn  up  the  tube  until  the  liquid  has  risen  above  the 
mark  c.  The  time  occupied  by  the  liquid  in  flowing  down 
the  tube  from  c  to  the  lower  mark,  d,  is  carefully  noted. 

The  capillary  tube  must  be  cleaned  with  the  utmost  care 
and  then  made  thoroughly  dry  before  beginning  the  experi- 
ment. Since  the  coefficient  of  viscosity  changes  on  an  aver- 
age of  two  per  cent,  for  each  degree,  care  must  be  taken  to 
insure  constant  temperature. 

This  is  insured  by  clamping  the  tube  in  a  thermostat 


VISCOSITY  AND  SURFACE   TENSION. 


47 


bath  such  as  the  one  shown  in  Fig.  20  of  the  preceding 
chapter.  a 

When  the  tube  has  remained  in  the  bath  suffi- 
ciently long  to  acquire  the  temperature  of  its 
surroundings  the  liquid  is  sucked  up  by  means  of 
a  piece  of  rubber  tubing  until  the  meniscus  is  a 
few  millimeters  above  the  upper  mark.  The  liquid 
is  then  allowed  to  flow  out,  the  time  of  passage 
from  the  upper  to  the  lower  mark  being  measured 
by  means  of  a  stop-watch.  The  observation 
should  be  repeated  several  times  and  if  possible 
with  two  or  more  tubes.  Before  using  the  tubes 
for  viscosity  determinations  it  is  of  course  necessary 
to  calibrate  them  by  means  of  water  at  a  definite 
temperature  in  order  to  get  the  constant  of  the  FIG.  23. 
tube.  The  following  table  contains  the  constants 
of  viscosity  for  water  at  different  temperatures : 


Temperature. 

0 

Poiseuille. 
0.018142 

10 

0.013351 

20 

0.010296 

30 

0.008212 

40 

0.006718 

Sprung. 

0.018136 
0.013271 
0.010214 
0.008186 
0.006725 


Traube. 

0.01824 

0.01333 

0.01032 

0.00819 

0.00669 


If  the  value  of  y  in  equation  (6)  is  sought  instead  of  the 
value  of  Q  in  equation  (7) ,  then  it  is  necessary  to  determine 
accurately  the  value  of  p,  V,  I,  and  p.  The  values  of  p  and 
V  are  accurately  measured  by  means  of  mercury  before  the 
apparatus  is  assembled.  The  clean,  dry  tube  is  fastened  to 
a  millimetre  scale  and  repeatedly  filled  as  full  as  possible 
with  clean  mercury.  The  lengths  of  the  mercury  threads 
are  measured,  due  care  being  taken  to  avoid  parallax.  If 
the  length  of  a  thread  is  I  mm.,  and  the  gain  in  weight  of 
the  tube  owing  to  the  addition  of  the  mercury  is  g  mg.;  and 


48  MEASUREMENTS. 

the  temperature  of  the  mercury  is  t,  then  the  radius  of  the 
tube  in  millimetres  is 

[<7(i  +  0.0001810 
p~  \  "    13.596^ 

The  value  of  the  pressure  p  is  calculated  as  follows :  Let  h^ 
be  the  height  of  the  lower  mark  above  the  opening  of  the  capil- 
lary tube,  and  let  h2  be  half  the  distance  between  the  two 
marks;  then  p  =  hl  +  hr  The  following  are  the  limits  to  the 
dimensions  of  the  several  parts  of  the  apparatus  which 
experience  has  shown  give  the  best  results: 

7  =  4  toSc.c.; 
(0  =  0.025  to  0.030  cm.; 
Z  =  30  to  40  cm.; 
h2  =  1  to  2  cm. 

(b)  Method  of  Coulomb. — Owing  to  the  many  experimental 
difficulties  which  beset  the  previous  method  and  to  its  lim- 
itation to  the  less  viscous  liquids,  the  method  of  Coulomb  is 
of  considerable  value  in  enabling  us  to  determine  relative 
or  specific  viscosities. 

If  a  heavy  disc  suspended  axially  by  a  light  vertical  wire 
be  immersed  in  a  liquid  and  then  set  into  torsional  vibration, 
the  ratio  of  any  two  successive  oscillations  in  the  same  direc- 
tion is  a  function  of  the  viscosity  of  the  liquid.  If  then  the 
disc  be  set  into  vibration  in  one  liquid  and  then  in  another, 
the  ratio  of  the  amplitude  of  successive  swings  in  the  same 
direction  for  each  liquid  will  enable  us  to  determine  the 
specific  viscosity.  If  rjl  be  the  coefficient  of  absolute  vis- 
cosity of  one  liquid,  rt  the  ratio  of  the  amplitudes  of  any  two 
successive  oscillations  in  the  same  direction  in  this  liquid, 
Tl  the  period  of  oscillation  of  the  disc,  and  yl  the  damping 
constant,  and  i?2,  rv  !F2,  and  f2  represent  the  corresponding 


VISCOSITY  AND  SURFACE.  TENSION. 


49 


quantities  for  the  other  liquid,  then  it  can  be  shown  mathe- 
matically that 

r^TVogr^ry 

T2     7\logr2     )?2 

The  apparatus  employed  is  shown  in  Fig.  24.      It  con- 
sists of  a  thin  vertical  wire  attached    by  one  end  to    a 


FIG.  24. 


rigid  frame,  while  the  other  end  is  attached  by  means  of  a 
heavy  vertical  rod  to  a  divided  circle  and  the  disc  which  is 
to  be  immersed  in  the  various  liquids.  The  vessel  in  which 


50  MEASUREMENTS. 

the  liquids  are  placed  is  surrounded  by  an  annular  space  in 
which  some  liquid  can  be  placed  to  maintain  an  approxi- 
mately .  constant  temperature  during  a  determination. 
After  the  liquid  to  be  examined  has  attained  the  desired 
temperature  the  disc  is  twisted  through  an  angle  of  about 
180°.  With  a  stop-watch  the  time  of  a  dozen  complete 
vibrations  is  taken.  From  this  result  the  time  T1  of  a  single 
vibration  can  be  calculated. 

We  now  take  a  series  of  readings  of  the  turning-points  of 
successive  vibrations  to  the  right  and  to  the  left.  The 
number  of  scale  divisions  through  which  the  disc  has  turned 
in  rotating  from  its  extreme  right  position  to  its  extreme  left 
is  the  amplitude  of  the  left  vibration.  Denoting  these  suc- 
cessive amplitudes  to  the  right  and  to  the  left  by  Liy  L2,  L3 
".  .  .  ,  and  R1}  R2,  R3  .  .  .  ,  we  have 


If  these  readings  were  taken  upon  the  standard  liquid  of 
reference,  then  in  a  precisely  similar  manner  the  values  of 
T2  and  r$  can  be  found  for  a  second  substance  which  may 
be  substituted  in  the  equation  previously  given,  and  the 
value  of  the  specific  viscosity  of  the  second  substance  deter- 
mined. This  method  is  of  most  value  in  working  with  oils 
or  other  extremely  viscous  liquids. 

Surface  Tension.  —  The  effect  of  the  unbalanced  molecular 
forces  within  a  liquid  acting  on  the  molecules  near  the  sur- 
face is  to  exert  a  pressure  on  the  interior  of  the  liquid  sim- 
ilar to  that  which  would  be  produced  by  an  elastic  mem- 
brane. This  pressure  is  clue  to  the  surface  tension  of  the 
liquid. 

If  a  capillary  tube  is  dipped  into  a  liquid  which  wets  it, 


VISCOSITY  AND  SURFACE   TENSION. 


51 


the  liquid  rises  within  the  tube  to  a  height  which  is  propor- 
tional to  the  surface  tension. 

Let  Fig.  25  represent  a  capillary  tube  dipping  into  a 
vessel  of  liquid.  The  weight  of  the  column  of  liquid  in  the 
tube  is  nr2hdg,  where  r  is  the  radius  of  the  tube;  h  the  height 


FIG.  25. 

of  the  liquid,  d  its  density,  and  g  the  acceleration  due  to 
gravity. 

The  force  which  balances  this  weight  of  liquid  is  the  ver- 
tical component  of  the  force  due  to  the  surface  tension  of 
the  liquid  surface  at  the  walls  of  the  tube.  If  7-  be  the  sur- 
face tension  and  0  the  angle  of  contact  of  the  liquid  with  the 
wall  of  the  tube,  then  this  vertical  component  is  27rr?-  cos  6. 
Therefore 


cos  0, 


or 


2y  cos  6 
dgr 


(D 


For  water  in  glass  tubes  #  =  0,  so  that  (1)  becomes 


dgr> 


(2) 


MEASUREMENTS. 


hdgr 

2" 


(3) 


Measurement  of  Surface  Tension. — A  very  satisfactory 
method  for  the  measurement  of  surface  tensions  is  that  de- 
vised by  Renard  and  Guye.*  The  arrangement  of  the 


(o) 


FIG.  26. 

apparatus  is  shown  in  Fig.  26.  A  test-tube  A  about  2  cm. 
in  diameter  is  closed  by  means  of  a  three-hole  rubber  stopper; 
through  the  first  hole  passes  a  thermometer  B,  through  the 
second  a  glass  tube  C  which  permits  free  access  of  air  to  the 
inside  of  the  test-tube  and  through  the  third  hole  passes  a 
glass  rod  D  which  fits  very  tightly.  Sealed  to  the  glass  rod 


*  Reynard  and  Guye,  Jour.  Chim.  Phys.,  V,  81,  1907. 


JNiv 

OF 


VISCOSITY  AND  SURFACE  TENSION. 


is  a  capillary  tube  E  having  an  opening  at  its  upper  end, 
while  the  lower  extremity  dips  beneath  the  surface  of  the 
liquid  G. 

Care  should  be  taken  to  select  a  capillary  with  a  uniform 
bore  and  to  mount  it  in  a  vertical  position. 

Having  filled  the  test-tube  with  the  liquid  to  be  inves- 
tigated, the  tube  A  is  placed  in  a  glass  heating-  jacket  con- 
taining some  liquid  whose  boiling-point  is  at  the  temperature 
at  which  the  surface  tension  is  required.  After  the  heating 
liquid  commences  to  boil,  the  thermometer  is  read  and  the 
boiling  is  continued  for  five  minutes.  If  after  this  interval 
of  time  the  thermometer  reading  remains  constant,  we  meas- 
ure the  rise  of  the  liquid  in  the  capillary  by  means  of  the 
cathetometer  and  then  slightly  raise  the  capillary  by  means 
of  the  rod  D. 

After  the  boiling  has  continued  for  five  minutes  longer 
we  again  read  the  thermometer,  and  if  no  change  has  taken 
place,  the  height  of  the  liquid  in  the  cap  llary  is  again  meas- 
ured. 

The  two  readings  of  h  should  not  differ  more  than  0.15  mm. 
The  radius  of  the  capillary  tube  having  been  obtained  from 
the  preliminary  calibration  and  knowing  the  density  of  the 
liquid  we  can  calculate  the  sunace  tension  by  means  of 
equation  (3). 

There  are  several  sources  of  error  in  the  method  to  which 
attention  should  be  directed;  they  are  as  follows: 

(1)  Erro  s  due  to  inclination  of  the  capillary  tube  from 
the  vertical.    This  source  of  error  is  rarely  greater  than  the 
errors  of  reading  the  height  of  the  liquid. 

(2)  Errors  due  to  the  omission  of  a  correction  factor  in 
the   formula   for  the  density   of   the  vapor-saturated   air. 
This  error  amounts  to  about  0.3  per  cent. 

(3)  Errors  due  to  the  expansion  of  the  capillary.    Up  to 


54  MEASUREMENTS. 

200°  this  amounts  to  about  0.4  per  cent.  Since  (2)  and  (3) 
act  in  opposition,  one  almost  compensates  the  other. 

Special  precautions  must  be  taken  to  insure  the  capillary 
tube  being  free  from  any  foreign  substances.  The  tube  is 
best  cleaned  by  drawing  chromic  acid  through  it  and  then 
washing  thoroughly  with  distilled  water. 

Relation  between  Surface  Tension  and  Molecular  Weight, 
—  In  1886  Eotvos  pointed  out  that  the  rate  of  change  of 
the  surface  energy  in  a  liquid  with  the  temperature  is  a 
constant. 

Measuring  the  temperature  from  the  critical  temperature 
as  zero  and  denoting  it  by  t  we  have 

drs 


In  order  that  we  may  work  with  comparable  quantities  s 
is  taken  as  the  molecular  surface  or  (Mv)%,  where  Mv  is  the 


molecular  volume.      The   equation  -  —  y,  —  =  c  was  tested 

ejt 

experimentally  by  Ramsay  and  Shields  who  found  that  for 
many  liquids  the  constant  c  had  a  value  varying  rom  2.04 
to  2.22,  or  an  average  -of  2.12.  It  is  thus  possible  by  this 
method  to  determine  the  molecular  weight  of  a  pure  liquid, 
provided  there  is  no  molecular  association.  To  do  this  we 
employ  the  formula 


In  cases  where  association  occurs  the  extent  of  this  can  be 
determined  by  the  surface  tension  method  Liquids  which 
do  not  give  a  value  for  c  approximating  2.12  for  different 


VISCOSITY  AND  SURFACE  TENSION.  55 

temperatures  are  known  to  be  associated.     Denoting  the 
degree  of  association  by  x  we  have 


2.12  /2.12\f 

_     or      x= 


In  the  case  of  associated  liquids  c  is  less  than  2.12. 


THERMAL  MEASUREMENTS. 


CHAPTER  V. 

THERMOMETRY. 

The  Mercury  Thermometer. — The  instrument  most  fre- 
quently employed  in  the  measurement  of  temperature  is 
the  mercury  thermometer.  To  make  a  complete  examina- 
tion of  this  instrument  both  skill  and  time  are  necessary, 
but  it  is  possible  to-day,  through  the  Physikalisch-Tech- 
nische  Reichsanstalt  or  through  the  United  States  Bureau 
of  Standards,  to  obtain  thermometers  which  have  been 
tested  most  carefully  in  every  respect.  Thus  it  is  assumed 
that  every  physico-chemical  laboratory  will  have  at  least 
one  corrected  standard  thermometer  with  which  all  other 
instruments  may  be  compared. 

It  is  only  necessary  then  to  give  the  method  for  the 
comparison  of  a  thermometer  with  the  laboratory  standard. 

Comparison  of  a  Thermometer  with  a  Standard  Ther- 
mometer.— The  two  instruments  are  placed  side  by  side  in  a 
good-sized  vessel  filled  with  some  fluid.  For  temperatures 
below  100°  C.  water  may  be  used,  between  100°  and  300° 
paraffin,  while  above  this  latter  temperature  a  mixture  of 
the  nitrates  of  sodium  and  potassium  is  adapted  to  the  pur- 
pose. The  temperature  of  the  bath  must  be  raised  very 
slowly  (about  1°  per  minute),  and  provision  must  be  made 

56 


THERMOMETRY.  57 

for  keeping  the  liquid  thoroughly  stirred.  The  readings 
should  be  taken  by  means  of  a  reading-telescope,  so  that 
tenths  of  a  division  may  be  estimated.  The  correction  for 
the  exposed  mercury  thread  is  negligible,  provided  each 
thermometer  projects  out  of  the  liquid  by  the  same  number 
of  degrees.  Furthermore,  if  each  thermometer  is  made  of 
the  same  kind  of  glass,  no  correction  need  be  introduced  for 
the  difference  hi  the  expansion  coefficients.  At  high  tem- 
peratures the  comparison  may  easily  be  inexact. 

Calibration  by  Means  of  a  Series  of  Fixed  Temperatures. — • 
Another  method  by  which  a  thermometer  may  be  examined 
between  0°  and  100°  involves  the  use  of  a  series  of  transition 
temperatures.* 

The  following  temperatures  may  be  obtained  at  the 
melting-points  of  the  corresponding  hydrates: 

Na2Cr04  +10H20 19°.63  C. 

Na2S04    +  10H20 32  .379 

Na2C03    +  10H20 35  .2 

Na2S203  +  5H20 47.9 

NaBr      +  2H20 50  .7 

MnCl2      +  4H20 57  .7 

Na3P04   +  12H20 73  .3 

Ba(OH)2+  8H20 77.9 

Correction  for  Unheated  Stem." — It  frequently  happens 
in  using  a  thermometer  that  the  whole  stem  of  the  instru- 
ment cannot  be  brought  to  the  temperature  to  be  measured. 
We  must  then  calculate  by  how  much  the  mercury  thread 
would  be  lengthened  were  it  all  to  be  brought  to  the  same 
temperature  as  the  bulb. 

*  Richards,  Zeit.  phys.  Chem.,  26,  690  and  28,  313. 


58  THERMAL  MEASUREMENTS. 

Let  a  =  coefficient  of  expansion  of  the  mercury =0.000 182; 
/?  =  "         "         "    "   glass       =0.000024; 

h= length  of  exposed  column  in  degrees; 
£0=mean  temperature  of  exposed  mercury  column; 
t  =  temperature  indicated. 

Then  the  correction,  C,  in  degrees  is 


If  differences  in  temperature  only  are  sought,  this  correction 
need  not  be  applied. 

The  Fixed  Points  of  the  Thermometer. — From  time  to 
time  it  is  well  to  test  the  so-called  fixed  points  of  a  thermome- 
ter. This  consists  of  two  operations:  (1)  determination  of 
the  freezing-point ;  (2)  determination  of  the  boiling-point. 

(1)  The  Freezing-point. — By  means  of  a  cork  fasten  the 
thermometer  in  a  test-tube  which  is  about  half  filled  with 
distilled   water,   taking   care   that   the   bulb   is    completely 
immersed.    The  tube,  which  is  provided  with  a  wire  stirrer, 
is  sunk  nearly  to  the  neck  in  a  mixture  of  ice  and  a  little 
salt,  the  water  being  cooied  about  a  degree  below  zero.    The 
stirrer  is  operated  slowly  until  ice  begins  to  separate,  when 
it  is  agitated  vigorously.    The  mercury  thread  rises   to  the 
zero-point  hi  about  a  minute,  and    remains  there  steadily. 
The  difference  between  the  reading  and  the  indicated    zero 
is  the  correction  to  be  applied.     The  Beckmann  freezing- 
point  apparatus,  to  be  described  in  a  later  chapter,  serves 
admirably  for  the  determination  of  the  freezing-point. 

(2)  The  Boiling-point. — The  determination  of  the  boiling- 
point  is  made  with  the  apparatus  shown  in  Fig.  27.    The 
thermometer  is  placed  in  the  steam-bath,  so  that  the  bulb 
and  as  much  of  the  stem  as  possible  are  surrounded  by  steam, 
but  care  must  be  taken  that  the  bulb  is  in  the  steam  and  not 


THERMOMETRY. 


59 


in  the  water.  After  the  thermometer  has  been  in  the  steam 
for  some  time  the  position  of  the  mercury  thread  is 
determined,  and  at  the  same  time  the  reading  of  the 
barometer  is  taken.  In  reading  the  barometer  the  height  of 
the  column  should  be  reduced  to  0°,  since  the  expansion 


FIG.  27. 

of  the  mercury  often  introduces  an  error  of  several  mil- 
limetres. 

The  height  of  the  barometer  is  given  by  the  height  of  a 
column  of  mercury  at  0°,  which  is  maintained  in  equilibrium 
by  gravity  and  the  atmospheric  pressure.  The  coefficient 
Df  expansion  of  mercury  is  0.000182,  so  that  if  h  be  the 
height  of  the  barometer  as  read  at  temperature  t,  its  value 
h',  reduced  to  0°,  is 

W  =  h  -0.000182-  h  -L 

On  account  of  the  expansion  of  the  scale  the  length  of  this 
also  must  be  reduced  to  normal  temperature.  If  /?  denotes 
the  coefficient  of  linear  expansion  of  the  scale,  the  com- 
plete expression  for  the  correction  of  the  barometer  reading 
becomes 

&'  =  h-  (0.000182  -p)ht. 


60  THERMAL  MEASUREMENTS. 

Having  obtained  the  corrected  barometer  reading,  the  tem- 
perature of  the  steam  is  found  from  the  tables. 

Without  the  tables  the  boiling-point  may  be  determined 
to  within  0°.l  for  all  pressures  between  715  and  770  mm. 
by  means  of  the  formula 

*=100°+0.0375(&-760). 

Illustration. — The  reduced  barometer  reading  is  742  mm. 
The  mercury  in  the  thermometer  stands  at  98°. 8.  The 
boiling-point  according  to  the  formula  is  t  =  100°  —  0.0375  •  18  = 
99.33.  Therefore  100°  is  denoted  by  the  division  98.8+ 
0.67-99.47,  or  the  boiling-point  as  marked  on  the  stem  is 
too  high  by  100- 99.47 =0°.53. 

Expansion. — The  coefficient  of  linear  expansion  is  the 
change  in  length  per  unit  of  length  of  a  body  for  a  change  of 
one  degree  in  temperature. 

The  coefficient  of  cubical  expansion  is  the  change  in 
volume  per  unit  of  volume  of  a  substance  for  a  change  of 
one  degree  in  temperature.  It  is  shown  in  text-books  of 
physics  that  the  coefficient  of  cubical  expansion  is  very 
nearly  three  times  the  coefficient  of  linear  expansion.  Since 
the  coefficient  of  expansion  usually  increases  with  increase 
in  temperature,  we  must  distinguish  between  the  true  coeffi- 
cient and  the  mean  coefficient,  which  is  determined  on  the 
assumption  that  the  expansion  is  uniform  for  each  interval 
of  temperature. 

The  determination  of  the  coefficient  of  cubical  expansion 
of  a  liquid  is  of  the  most  importance  to  the  physical  chemist. 

Determination  of  the  Coefficient  of  Cubical  Expansion  of 
Glass  and  Liquids. — Let  d  and  d^  denote  the  densities  and 
v  and  vl  the  volumes  of  a  liquid  at  the  temperatures  t  and  tlt 
and  let  a  represent  the  coefficient  of  cubical  expansion. 
Then  we  have 


THERMOMETRY.  61 

hence 


or 


d-d, 

" 


From  this  we  see  that  the.  coefficient  of  cubical  expansion 
may  be  calculated  from  two  determinations  of  the  density 
at  two  different  temperatures. 

The  formula  usually  given  for  the  calculation  of  the  coeffi- 
cient of  cubical  expansion  is 

w        1     w—wl 

where  w  and  w1  denote  the  weights  of  liquid  contained  in 
the  pyknometer  at  the  two  temperatures  t  and  tl}  and  where 
P  is  the  coefficient  of  cubical  expansion  of  the  glass.  When 
P  is  known,  then  two  weighings  of  the  pyknometer  at  tem- 
peratures t  and  tl  are  sufficient  for  the  determination  of  a. 
On  the  average  /?  may  be  placed  equal  0.000024. 

If  the  value  of  /?  is  sought,  however,  the  pyknometer  is 
filled  with  pure  mercury  and  weighed  at  two  temperatures, 
t  and  t,.  The  coefficient  of  expansion  of  pure  mercury  may 
be  taken  as  0.000182.  Then  we  have 

1     w—w. 


w      t^  —  t       w 

The  pyknometer  is  filled  with  mercury  by  dipping  the  point 
under  the  surface  and  alternately  heating  and  cooling  the 
pyknometer. 

The  apparatus  used  in  determining  the  coefficient  of 
cubical  expansion  of  a  liquid  is  shown  in  Fig.  28.  The  pyk- 
nometer (Fig.  28)  is  to  be  placed  in  a  thermostat  and  heated 
to  two  different  temperatures. 


62 


THERMAL  MEASUREMENTS. 


The  pyknometer  (Fig.  29)  is  to  be  heated  in  the  vapor 
of  boiling  water  and  ether  in  the  device  shown  in  Fig.  30, 
the  method  being  that  due  to  R.  Schiff.* 

By  means  of  an  iron  spoon  the  pyknometer  is  placed  in  a 


FIG.  28. 


FIG.  29. 


FIG.  30. 


conical-shaped  vessel,  which  is  heated  by  the  vapor  of  the 
liquid  boiling  in  the  vessel  below. 

The  pyknometer  is  covered  with  a  glass  tube  of  the 
form  shown,  into  which  the  liquid  overflows  from  the  pyk- 
nometer. The  volume  of  the  pyknometer  at  34°  is  obtained 
from  weighing  the  mercury  which  it  contains  after  heating 
in  the  vapor  of  boiling  ether.  By  weighing  a  second  time 


*  R.  Schiff,  Berichte  d.  d.  chem.  Ges.,  18,  p.  1539,  1885. 


THERMOMETRY.  63 

after  heating  in  the  vapor  of  boiling  water  the  coefficient  of 
expansion  ft  can  be  calculated. 

The  volume  at  0°  can  be  calculated  approximately  from 
the  formula 


"'-!+#• 

If  the  coefficient  of  expansion  of  the  liquid  is  known,  the 
coefficient  of  cubical  expansion  is  calculated  from  the  for- 
mula 


w 
"" 


The  pyknometer  when  filled  is  heated  in  the  vapors  of  appro- 
priate liquids. 

By  determining  the  coefficients  of  expansion  of  a  liquid 
at  different  intervals  of  temperature  the  relation  between 
a  and  t  is  expressed  by  the  formula 

a  =  a+bt+ct2, 

where  a,  b,  and  c  are  constants  determined  by  substituting 
the  corresponding  values  for  a  and  t. 

Molecular  Volumes  of  Liquids  at  their  Boiling-points.  — 
Closely  allied  to  the  determination  of  the  coefficient  of  ex- 
pansion of  a  liquid  is  the  determination  of  molecular  volume 
at  the  boiling-point.  The  method  due  to  Ramsay  and  Lothar 
Meyer  is  the  most  convenient. 

The  pyknometer  is  weighed  filled  with  air,  then  with 
distilled  water  at  room  temperature,  and  then  at  the  tem- 
perature of  boiling  water. 

Let  wt  =  weight  of  water  at  temperature  t; 
wtl=      "      "      "     "  "  *,; 

Vt,  vtlj  dt,  and  dtl  be  the  corresponding  volumes  and 
densities. 


64  THERMAL  MEASUREMENTS. 

Then  we  have 

wt  wtl 

v*  =  :r    anc*    ^i  =  7T 

Hence 

wtl     we 

and 

~    Vtt—Vt    dtl     dt 

assuming  /?  =  0.000024. 

The  volume  for  any  boiling-point  0  between  t  and  ^  is 


Let  6  =  boiling  of  liquid  of  which  molecular  volume  is 

desired; 

d0=its  density  at  #°; 
ify=its  weight  at  <9°  =  [(pyk.  +  liq.)  —  (pyk.  +  air)]; 

and 

vg=  volume  of  the  pyknometer  at  temperature  6°. 
The  molecular  volume  is  then 

m 


where  m  is  the  molecular  weight  of  the  substance. 

The  pyknometer  (Fig.  31)  is  made  of  Jena  glass  and 
holds  about  2.5  c.c.  The  larger  closed  bulb  is  connected  with 
a  rather  narrow  capillary  tube,  the  end  of  which  is  turned 
back  upon  itself. 

The  pyknometer  is  filled  with  the  liquid  under  examina- 
tion by  means  of  the  apparatus  shown  in  Fig.  32. 


THERMOMETRY. 


65 


A  wide  test-tube  closed  with  a  well-fitting  rubber  stopper 
is  connected  with  an  exhaust-pump  and  the  outside  air  by 
means  of  a  branched  side  'tube  provided  with  two  stop-cocks. 
A  calcium-chloride  tube  is  inserted  in  the  branch  communi- 


FIG.  31. 


FIG.  32. 


eating  with  the  air.  The  bottom  of  the  test-tube  is  filled 
with  the  liquid,  and  by  means  of  a  wire  passing  air-tight 
through  the  stopper  the  pyknometer  is  lowered  until  the 
point  of  the  capillary  is  immersed.  By  alternately  opening 
the  stop-cocks  to  the  pump  and  the  outside  air  the  pyk- 
nometer is  filled  with  the  exception  of  a  very  small  air- 
bubble,  which  can  be  made  to  disappear  upon  subsequent 
heating. 

If  the  liquid  is  heated  at  the  same  time  that  the  air  is 
alternately  exhausted  and  readmitted,  the  time  of  filling  is 
shortened. 

The  pyknometer  is  emptied  by  means  of  the  same  appa- 
ratus. It  is  suspended  in  an  inverted  position,  and  the  two 
stop-cocks  are  alternately  opened  and  closed.  The  pyknom- 
eter is  dried  by  means  of  alcohol  and  ether. 


66  THERMAL  MEASUREMENTS. 

When  the  vessel  is  filled  it  is  hung  in  a  boiling-vessel 
by  means  of  a  fine  platinum  wire  which  passes  through  the 
stopper.  The  boiling-vessel  is  provided  with  a  reflux  con- 
denser, which  if  desired  may  be  connected  with  a  pressure- 
regulator. 

For  liquids  which  bump  when  boiling  a  capillary  tube  is 
passed  through  the  cork  and  a  current  of  air  is  gently  drawn 
through  the  liquid. 

The  process  in  brief  then  is  as  follows:  The  pyknometer 
when  filled  with  the  liquid  is  suspended  in  the  flask,  so  that 
the  point  of  the  capillary  tube  remains  in  the  vapor.  The 
liquid  in  the  pyknometer  expands  and  drops  out  of  the  tube, 
expelling  with  it  the  remaining  air-bubble.  When  it  has 
acquired  the  temperature  of  the  surrounding  vapor  and  no 
more  liquid  is  expelled  the  boiling  is  stopped  and  the  pyk- 
nometer allowed  to  cool.  When  the  pyknometer  has  ac- 
quired the  temperature  of  the  room  it  is  removed,  carefully 
dried  and  then  weighed. 


CHAPTER  VI. 

MELTING-  AND  BOILING-POINTS. 

Melting-point. — The  determination  of  the  melting-point 
is  one  of  the  commonest  operations  of  the  chemical  labora- 
tory, and  yet  the  method  usually  employed  is  by  no  means 
accurate.  The  values  obtained  show  variations  of  from  1°  to 
2°.  These  variations  may  be  ascribed  to  the  use  of  capillary 
tubes  of  too  small  diameter. 

The  most  accurate  method,  however,  cannot  always  be 
employed  owing  to  scarcity  of  material,  and  hence  the  usual 
method  of  melting  in  a  capillary  tube  attached  to  the  stem 
of  a  thermometer  must  be  resorted  to.  In  the  laboratory  of 
the  physical  chemist,  however,  there  is  generally  sufficient 
material  at  hand  to  permit  of  the  employment  of  more  accu- 
rate means. 

A  test-tube  of  about  3  crn.  diameter  is  furnished  with  a 
carefully  calibrated  thermometer  and  a  platinum  stirrer, 
and  in  this  is  placed  15  to  20  grams  of  the  substance. 
The  test-tube  is  then  placed  in  a  large  beaker  containing 
some  suitable  liquid  which  can  be  heated  several  degrees 
above  the  melting-point  of  the  substance.  Water,  oil,  sul- 
phuric acid,  paraffin,  concentrated  solutions  of  sodium 
chloride,  calcium  chloride,  etc.,  may  be  used.  The  liquid 
is  heated  several  degrees  above  the  melting-point  of  the 
substance,  which  has  been  roughly  determined  by  the  ordi- 
nary capillary- tube  method. 

67 


68  THERMAL  MEASUREMENTS. 

As  soon  as  the  substance  begins  to  melt  it  is  stirred 
constantly.  So  long  as  any  solid  remains  present  the  ther- 
mometer will  remain  stationary.  This  temperature  is  read 
and  corrected  for  the  exposed  thread  of  mercury.  By  this 
method  it  is  possible  to  attain  an  accuracy  of  0°.l  C. 

If  more  material  is  at  the  disposal  of  the  experimenter, 
say  50  grams,  it  is  possible  to  determine  the  solidifying 
point  with  great  accuracy. 

The  beaker  is  replaced  by  a  thermostat  bath,  which  is 
maintained  about  2°  below  the  solidifying  point  of  the  sub- 
stance. When  the  substance  has  been  melted  the  test-tube 
is  immersed  in  the  thermostat  bath  and  allowed  to  under- 
cool.  After  sufficient  time  has  elapsed  to  insure  the  under- 
cooling of  the  substance  a  small  particle  of  the  solid  is 
thrown  into  the  molten  substance.  Solidification  at  once 
results  and  the  thermometer  rises  to  the  true  temperature 
of  solidification. 

i  There  is  perhaps  no  determination  upon  which  the  or- 
ganic chemist  places  greater  reliance  than  upon  that  of  the 
melting-point  of  a  compound,  and  yet  the  values  obtained 
are  by  no  means  as  accurate  as  at  first  sight  appears.  The 
student  is  specially  referred  on  this  point  to  Wiedemann 
and  Ebert,  Physikalisches  Praktikum,  4th  Edition,  p.  159. 

Boiling-point. — The  boiling-point  of  a  liquid  is  the  tem- 
perature at  which  its  vapor  pressure  and  the  external  atmos- 
pheric pressure  are  in  equilibrium. 

Since  the  boiling-point  is  a  function  of  the  external 
pressure,  it  is  customary  to  consider  the  temperature  at 
which  a  liquid  boils  under  760  mm.  pressure  as  the  normal 
..boiling-point. 

The  arrangement  of  Berthelot  (Fig.  33)  serves  admirably 
for  the  determination  of  the  boiling-point.  The  thermome- 
ter is  placed  in  a  long-necked  flask  the  neck  of  which  is  sur- 


MELTING-  AND  BOILING-POINTS. 


69 


rounded  with  a  wide  tube,  as  shown  in  the  illustration.  The 
liquid  is  placed  in  the  flask,  which  has  been  carefully  cleaned, 
and  the  calibrated  thermometer  inserted  in  the  cork  so  far 


FIG  33. 

that  no  correction  need  be  applied  for  the  unheated  stem. 
The  bulb  under  no  circumstances  should  dip  beneath  the 
surface  of  the  liquid.  Correction  must  be  made  for  the  baro- 
metric pressure.  Denoting  the  barometric  pressure  by  b 
and  the  observed  temperature  by  t,  the  normal  boiling- 
point  is  nearly  £+0.0375(760-6).  Should  the  boiling-point 


70  THERMAL  MEASUREMENTS. 


be  desired   to   the  j^  of  a   degree,  the  Jones   apparatus 
(p.  72)  should  be  employed. 

For  the  determination  of  the  boiling-point  under  vary- 
ing pressures  see  Roloff,  Zeit.  phys.  Chem.,  11,  p.  25,  1893. 

Depression  of  the  Freezing-points  of  Solvents  by  Dissolved 
Substances.  —  In  1788  Blagden  showed  that  the  freezing- 
point  of  a  solvent  is  depressed  by  the  addition  to  it  of  any 
soluble  substance. 

Raoult  found  in  1887  that  "  if  one  molecule  of  any  sub- 
stance is  dissolved  in  100  molecules  of  any  liquid  of  a  differ- 
ent nature,  the  lowering  of  the  freezing-point  of  this  liquid 
is  always  nearly  the  same.  " 

Let  M  =  molecular  weight  of  the  dissolved  substance; 
g  =  number  of  grams  of  dissolved  substance; 
G  =  number  of  grams  of  solvent;  and 
J  =  the  observed  depression. 
Then  we  have 


where  C  is  a  constant  for  the  solvent  used.  The  value  of  C 
may  be  found  experimentally  by  using  as  a  dissolved  sub- 
stance a  compound  of  which  the  molecular  weight  is  known. 
The  value  of  C  may  also  be  calculated  by  means  of  the  equa- 
tion 

27^ 

100L' 

For  the  derivation  of  this  equation  the  student  is  referred 
to  any  good  text-book  of  physical  chemistry. 

Apparatus  and  Method.  —  The  apparatus  employed  in 
determining  the  depression  of  the  freezing-point  is  that 
designed  by  Beckmann,  shown  in  Fig.  34.  It  consists  of  a 
Stout  test-tube,  A,  provided  with  a  side  tube,  a  thermome- 


MELTING-  AND  BOILING-POINTS. 


71 


51 


FIG.  34. 


FIG.  35. 


72  THERMAL  MEASUREMENTS. 

ter  and  stirrer.  This  stirrer  consists  of  a  ring  of  platinum- 
foil  soldered  to  a  thick  platinum  wire,  or  it  may  be  made  by 
bending  a  glass  rod  into  a  circle  of  sufficient  diameter  to 
allow  the  thermometer-bulb  to  pass  through.  By  means  of 
a  cork  this  tube  is  fastened  into  a  wider  tube,  B,  which  is 
supported  in  the  large  vessel  C  by  means  of  a  metallic 
cover.  The  vessel  C,  which  is  also  furnished  with  a  stirrer, 
contains  the  freezing-mixture.  To  prevent  too  rapid  melt- 
ing of  the  ice,  C  should  be  wrapped  in  felt  or  some  other 
insulating  material.  The  air-space  between  B  and  A  serves 
to  prevent  too  rapid  or  unequal  cooling  of  the  solution  to  be 
frozen.  For  accurate  determinations  the  thermometer  must 
be  graduated  to  -fa  or  yi^  of  a  degree. 

The  thermometer  designed  by  Beckmann  (Fig.  35)  is 
best  adapted  to  this  work.  Since  the  Beckmann  thermome- 
ter is  of  special  value  in  the  physico-chemical  laboratory,  a 
brief  description  of  it  is  given  here. 

This  thermometer  is  a  differential  instrument — that  is,  it 
cannot  be  used  for  the  determination  of  absolute  tempera- 
tures, but  only  for  the  measurement  of  differences  of  tem- 
perature, such  as  the  lowering  of  the  freezing-point  of  water 
by  a  dissolved  substance.  In  the  accompanying  illustration 
(Fig.  36)  is  shown  the  characteristic  part  of  the  thermometer. 

By  means  of  this  reservoir  at  the  upper  end  of  the  instru- 
ment the  quantity  of  mercury  in  the  thermometer-bulb  can 
be  increased  or  decreased,  and  thus  the  zero  of  the  scale  can 
be  set  at  any  arbitrary  division.  This  adjustment  of  the 
amount  of  mercury  in  the  bulb  is  accomplished  by  tapping 
or  throwing  the  mercur}r  either  from  the  top  or  the  bottom 
of  the  reservoir.  With  a  little  practice  the  experimenter 
soon  acquires  the  necessary  skill  in  "  setting "  his  ther- 
mometer. 

The  total  range  of  such  a  thermometer  is  usually  5°  or  6°. 


MELTING-  AND  BOILING-POINTS. 


73 


Each  degree  is  divided  into  tenths  and  hundredths.  Such 
thermometers  can  be  used  for  both  freezing-point  and  boil- 
ing-point determinations. 

The  first  step  in  determining  the  depression  of  the  freez- 
ing-point consists  in  the  determination  of  the  freezing-point 
of  the  pure  solvent. 

The  inner  tube,  A,  is  accurately  weighed  and  then  sup- 


FIG.  36. 

plied  with  15  or  20  grams  of  the  solvent,  care  being  taken  to 
keep  the  neck  of  the  tube  dry.  After  the  introduction  of 
the  solvent  the  tube  is  again  weighed  accurately  to  centi- 
grams. The  tube  is  then  placed  in  a  vessel  containing  ice 
and  salt  or  some  other  suitable  freezing-mixture,  and  the 
solvent  frozen.  The  tube  is  then  removed  from  the  freezing- 
mixture,  and  the  solidified  solvent  is  just  melted  by  holding 
the  tube  in  the  hand  and  slowly  operating  the  stirrer.  When 
the  solvent  is  melted  the  tube  is  placed  in  the  air-jacket  B, 
and  with  frequent  stirring  the  solvent  is  again  frozen.  The 


74  THERMAL  MEASUREMENTS. 

thermometer  usually  falls  several  tenths  of  a  degree  below 
the  freezing-point,  due  to  the  undercooling  of  the  liquid. 

Freezing  may  be  brought  about  by  dropping  into  the 
liquid  a  minute  crystal  of  the  solid  phase.  As  soon  as  crys- 
tallization begins  the  thermometer  rises  rapidly,  and  after 
thirty  to  sixty  seconds  attains  a  maximum,  which  is  taken 
as  the  freezing-point  of  the  solvent.  Before  reading  the 
thermometer  it  should  be  gently  tapped,  with  a  pencil  or 
with  a  cork  on  the  end  of  a  glass  rod,  to  overcome  the  friction 
of  the  mercury  thread  in  the  capillary. 

The  degree  of  undercooling  should  never  be  allowed  to 
exceed  one  degree,  since  otherwise  errors  are  introduced. 
On  the  other  hand,  sufficient  separation  of  ice  will  not  occur 
unless  0°.5  undercooling  takes  place.  For  accurate  work  the 
apparatus  should  not  be  set  up  in  a  room  the  temperature 
of  which  differs  more  than  a  few  degrees  from  the  freezing- 
point  of  the  solvent. 

The  temperature  of  the  freezing-bath  should  not  be  more 
than  5  or  6  degrees  below  the  freezing-point  of  the  liquid 
under  investigation. 

When  the  freezing-point  of  the  solvent  is  determined 
the  solute  is  introduced  into  the  tube  A. 

Solids  are  usually  weighed  in  glass-stoppered  weighing- 
tubes  by  means  of  which  they  are  introduced  into  A. 

Liquids  may  be  introduced  most  conveniently  by  means 
of  the  capillary  pipette  shown  in  Fig.  37.  The  pipette  is 
weighed  before  and  after  the  introduction  of  the  liquid. 

The  determination  of  the  freezing-point  of  the  solution 
then  follows.  It  is  carried  out  exactly  as  for  the  pure  sol- 
vent. 

After  making  a  series  of  determinations  of  freezing- 
points  of  solutions  the  freezing-point  of  the  pure  solvent 
must  be  redetermined. 


MELTING-  AND  BOILING-POINTS. 


75 


The  freezing-mixture  employed  varies  with  the  solvent 
or  solution  under  investigation. 

For  water  and  aqueous  solutions  mixtures  of  snow  and 
ice  are  most  satisfactory;  for  benzene  mixtures  of  ice  and 
water  are  sufficient;  for  acetic  acid  the  bath  consists  of 
water  and  a  little  ice;  while  for  solvents,  such  as  phenol 
and  naphthalene,  an  ordinary  thermostat  is  sufficient. 


FIG.  37. 

For  hygroscopic  solvents,  such  as  acetic  acid,  special  pre- 
cautions must  be  taken  to  protect  them  from  the  moisture 
of  the  air. 

The  method  as  above  outlined  is  essentially  that  given 
by  Beckmann.  It  is  sufficiently  accurate  for  the  determina- 
tion of  molecular  weights,  the  molecular  weight  found  being 
within  5%  of  the  true  value.  For  accurate  determinations 
the  method  of  Raoult  must  be  employed,  when  with  care 
the  depression  of  the  freezing-point  may  be  determined  to 
0.001  of  a  degree. 

The  values  of  the  constants  for  the  more  important  sol- 
vents are  here  given: 


76  THERMAL  MEASUREMENTS. 

Solvent.  Constant. 

Water 18.5 

Acetic  acid 39 .0 

Benzene 50.0 

Phenol 75.0 

Naphthalene 70.0 

Formic  acid 27 . 7 

Nitrobenzene 70.0 

Ethlyene  bromide 118.0 

Dissociation  by  the  Freezing-point  Method. — As  is  well 
known,  the  molecular  depression  of  the  freezing-point  of 
water  produced  by  all  non-electrolytes  is  a  constant,  18.5. 
That  is,  all  undissociated  substances  give  a  molecular  de- 
pression of  18.5.  All  electrolytes,  however,  produce  a  molec- 
ular lowering  of  the  freezing-point  of  water  greater  than 
18.5.  This  increase  in  the  molecular  lowering  is  due  to  the 
dissociation  of  the  dissolved  substance. 

The  ratio  of  the  observed  molecular  lowering  to  18.5  is 
the  coefficient  i,  introduced  by  Van't  Hoff  in  the  gas  equa- 
tion, expressing  the  relation  between  the  number  of  mole- 
cules actually  present  in  the  solution  to  the  number  which 
would  have  been  present  had  no  dissociation  occurred. 

If  n  gram-molecules  of  a  substance  are  weighed  out  and 
dissolved  in  water,  if  a  is  the  percentage  of  n  which  is  dis- 
sociated, and  z  is  the  number  of  parts  into  which  a  molecule 
of  the  substance  breaks  down,  then  we  have  in  solution 
n—na  molecules  and  zna  parts  of  molecules.  Therefore 

n— na  +  zna 
*• £ !+(«-!)«, 

or 

t-1 


MELTING-  AND  BOILING-POINTS.  77 

This  equation  enables  us  to  calculate  the  dissociation  from 
freezing-point  measurements. 

Elevation  of  the  Boiling-points  of  Solvents  by  Dissolved 
Substances. — It  has  long  been  known  that  the  vapor  pres- 
sure of  a  solution  is  lower  than  the  vapor  pressure  of  the 
pure  solvent.  Babo  and  Wiillner  found  that  the  lowering 
of  the  vapor  tension  is  proportional  to  the  amount  of  solute 
present;  and  for  the  same  solution  the  depression  for  any 
temperature  is  the  same  fraction  of  the  vapor  tension  of  the 
pure  solvent. 

It  was  Raoult,  however,  who  showed  that  one  gram-mole- 
cule of  any  substance  dissolved  in  100  gram-molecules  of  any 
solvent  causes  a  constant  relative  depression  of  the  vapor  ten- 
sion or  elevation  of  the  boiling-point. 

This  relation  is  entirely  analogous  to  the  relation  between 
the  lowering  of  the  freezing-point  and  the  quantity  of  solute 
in  a  definite  quantity  of  solvent.  The  value  of  the  molecular 
weight  of  the  solute  in  the  given  solvent  is  given  by  the 
formula 


where  C  is  the  constant  for  the  solvent,  p  the  observed  rise 
in  the  boiling-point  of  the  solvent,  g  the  weight  of  solute, 
and  G  the  weight  of  solvent. 

Here,  as  in  the  freezing-point  method,  the  value  of  C  may 
be  determined  either  experimentally  or  by  means  of  the 
thermodynamic  relation 

2T72 
~100L' 

where  L  denotes  the  latent  heat  of  vaporization  of  the  sol- 
vent. 


78  THERMAL  MEASUREMENTS. 

Apparatus  and  Method. — Of  the  many  forms  of  boiling- 
point  apparatus  which  have  been  devised,  perhaps  the  most 
convenient  and  accurate  is  that  of  Jones. 

This  apparatus  is  shown  in  Fig.  38. 

Into  the  glass  boiling-tube  A  are  introduced  some  glass 
beads,  while  to  the  side  tube  Al  the  condenser  C  is  attached. 
Into  the  beads  a  platinum  cylinder,  P,  is  inserted  by  placing 
the  finger  upon  the  top  of  the  cylinder  and  gently  shaking 
A.  When  the  cylinder  P  is  in  place  several  bits  of  plati- 
num-foil with  the  corners  bent  alternately  in  and  out  are 
dropped  upon  the  beads  at  G.  The  liquid  whose  boiling- 
point  is  to  be  determined  is  introduced  into  A  until  the  bulb 
of  the  thermometer  is  covered,  as  shown  in  the  illustration. 
The  liquid  must  not  come  within  a  centimetre  and  a  half  of 
the  top  of  the  platinum  cylinder.  The  tube  A  is  surrounded 
with  an  asbestos  jacket,  M,  and  rests  on  an  asbestos  board 
in  which  a  circular  hole  is  cut  and  over  which  is  laid  a  sheet 
of  wire  gauze. 

The  tube  A  is  heated  by  means  of  a  Bunsen  burner  pro- 
vided with  a  conical  chimney.  The  flame  used  must  be  very 
small. 

If  the  solvent  is  hygroscopic,  it  may  be  protected  from 
moisture  by  closing  the  mouth  of  the  condenser-tube  with  a 
calcium-chloride  tube. 

In  making  a  determination  of  the  boiling-point  the  first 
step  is  the  adjustment  of  the  thermometer,  so  that  the  top 
of  the  mercury  thread  comes  to  rest  on  the  lower  portion  of 
the  scale  when  the  bulb  is  immersed  in  the  boiling  solvent. 
This  is  effected  by  pouring  some  solvent  into  the  tube  A, 
inserting  the  thermometer,  and  heating.  When  the  solvent 
is  boiling  and  as  much  mercury  has  been  driven  over  into 
the  reservoir  of  the  thermometer  as  is  possible,  the  ther- 
mometer is  removed  from  the  liquid,  inverted  for  an  instant, 


FIG.  38. 


80  THERMAL  MEASUREMENTS. 

and  then  brought  back  to  a  normal  position  and  given  a 
tap  sharp  enough  to  cause  the  mercury  to  fall  from  the  top 
to  the  bottom  of  the  reservoir.  The  thermometer  is  then 
replaced  in  the  apparatus,  and  the  mercury  thread  allowed 
to  become  stationary.  If  the  setting  is  as  desired,  the  appa- 
ratus is  ready  for  a  determination ;  but  if  not,  the  above  pro- 
cess is  repeated  until  the  mercury  comes  to  rest  within  the 
first  two  degrees  of  the  scale.  Here,  as  with  the  adjustment 
of  the  thermometer  for  the  freezing-point  method,  a  little 
practice  is  necessary  before  the  thermometer  can  be  adjusted 
rapidly  and  satisfactorily.  After  the  thermometer  has  been 
adjusted  it  is  removed  and  the  stem  is  carefully  dried.  The 
beads  and  platinum  clippings  are  removed  from  A,  and  are 
carefully  dried  with  alcohol  and  ether.  The  tube  A  and  the 
platinum  cylinder  are  also  freed  from  adhering  solvent. 
The  glass  beads  are  then  poured  into  the  tube,  the  platinum 
cylinder  inserted  and  pressed  down  into  the  beads,  and  then 
the  platinum  clippings  dropped  into  the  platinum  cylinder. 
The  neck  of  the  tube  A  is  then  closed  with  a  ground-glass 
stopper,  and  the  side  tube  closed  with  a  cork.  The  whole  is 
then  placed  in  a  beaker  and  weighed  to  centigrams.  The 
solvent  is  then  introduced,  and  the  apparatus  is  weighed 
again.  After  the  solvent  is  weighed  the  apparatus  is  assem- 
bled as  shown  in  the  illustration,  and  the  boiling-point  of 
the  pure  solvent  determined.  The  size  of  the  flame  must 
be  very  carefully  regulated,  so  that  the  boiling  is  vigorous 
but  not  violent.  This  is  best  attained  by  means  of  a  screw 
pinch-cock  on  the  gas  tubing.  Some  time  is  necessary  for 
the  establishment  of  the  equilibrium  temperature  between 
the  pure  solvent  and  its  vapor.  When  the  mercury  column 
is  stationary  the  thermometer  is  tapped  gently  with  a  pencil 
or  special  hammer  and  the  reading  taken.  Great  care 
should  be  taken  to  read  the  thermometer  only  when  the 


MELTING-  AND  BOILING-POINTS.  81 

mercury  thread  is  rising.  Indeed  this  is  a  general  rule  of 
thermometry.  When  the  boiling-point  of  the'  pure  solvent 
has  been  established  a  tube  containing  the  solute  pressed 
into  pellets  is  weighed,  and  a  suitable  number  of  these  poured 
into  the  solvent.  Of  course  the  solvent  should  be  allowed 
to  cool  before  removing  the  stopper  for  the  introduction  of 
the  solute,  otherwise  the  solvent  will  escape  as  vapor.  The 
weighing-tube  is  then  reweighed,  and  the  amount  of  sub- 
stance introduced  thus  ascertained.  The  boiling-point  of 
the  solution  is  determined  in  exactly  the  same  way  as  the 
boiling-point  of  the  pure  solvent.  It  usually  takes  less 
time  for  the  attainment  of  equilibrium  with  a  solution  than 
with  the  pure  solvent. 

It  is  obvious  that  in  all  boiling-point  determinations  the 
barometer  must  be  carefully  observed. 

If  the  determination  of  the  boiling-point  of  the  solution 
is  made  quickly  after  the  boiling-point  of  the  solvent  has 
been  ascertained,  no  correction  is  necessary  for  change  in 
pressure,  since  it  will  be  so  small.  In  making  a  series  of  deter- 
minations it  will  be  found  convenient  to  set  up  two  pieces 
of  apparatus,  in  one  of  which  the  pure  solvent  is  kept  con- 
stantly boiling.  In  this  way  we  are  made  independent  of 
changes  in  atmospheric  pressure.  A  small  correction  should 
be  introduced  for  the  evaporation  and  condensation  in  the 
condenser.  According  to  Beckmann  the  amount  of  liquid 
suspended  in  the  boiling-tube  is,  for  very  mobile  liquids, 
from  0.15  to  0.2  gm.,  while  for  water  it  is  about  0.35  gm. 

The  following  table  gives  the  values  of  the  boiling-point 
and  the  boiling-point  constant  for  the  most  common  sol- 
vents: 


82  THERMAL  MEASUREMENTS. 

Solvent.                                                  Boiling-point.  Constant. 

Ethyl  ether 34° .  97  21.6 

Carbon  disulphide 46  . 2  23 . 5 

Acetone 56  . 3  17.2 

Chloroform 61  . 2  35 .9 

Ethyl  acetate 74  . 6  26 . 8 

Ethyl  alcohol 78  .3  11 .7 

Benzene 80  .3  26. 1 

Water 100.0  5.1 

Acetic  acid 118  .1  25.3 

Ethylene  bromide 131  . 6  64 . 5 

Phenol 132  .3  30.4 

Anilin.,                                                 .  182  32.2 


Molecular  Weight  by  the  Method  of  Longinescu. — Re- 
cently G.  G.  Longinescu  *  has  pointed  out  a  very  simple 
method  for  the  determination  of  the  molecular  weights  of 
pure  solids  and  liquids.  If  T  denote  the  absolute  boiling- 
point  of  a  pure  liquid,  and  D  be  its  density  then  the  number 
of  atoms  in  the  molecule  is  given  by  the  formula 


\100X 

Again,  if  T  denote  the  absolute  melting-point  of  a  solid, 
and  its  density  be  D,  then  the  number  of  atoms  in  the  mole- 
cule is 

T     \2 
n 


This  method  is  of  great  value  in  checking  the  determina- 
tions of  the  molecular  weights  of  pure  liquids  made  by  the 
surface  tension  method  of  Ramsay  and  Shields. 

*  Jour.  Chim.  Phys.,  I.  289,  296,  391,  1903. 


CHAPTER  VII. 

CALORIMETRY. 

Quantity  of  Heat. — In  order  to  measure  the  quantity  of 
heat  which  is  lost  or  gained  by  a  body  when  its  temperature 
changes  or  when  its  physical  state  changes,  the  unit  com- 
monly employed  is  that  quantity  of  heat  which  acting  on  a 
given  mass  of  water  alters  its  temperature  by  a  definite 
amount.  Since  the  specific  heat  of  water  is  not  the  same 
for  all  temperatures,  it  is  necessary  to  specify  between  what 
two  temperatures  the  water  is  to  be  taken.  The  following 
units  are  all  in  use: 

(1)  The  heat  required  to  raise  1  gram  of  water  from  0°  C. 
to  1°  C. 

(2)  The  heat  required  to  raise   1  gram  of  water  from 
3°.5  C.  to  4°.5  C. 

(3)  The  heat  required  to  raise  1  gram  of  water  from 
14°.5  C.  to  15°.5  C. 

(4)  The  heat  required  to  raise  1  gram  of  water  from 
18°.0  C.  to  19°.0  C. 

(5)  The  heat  required  to  raise  1  gram  of  water  from 
0°  C.  to  100°  C. 

Each  of  these  units  is  called  a  calorie. 

It  is  obviously  necessary  to  specify  what  calorie  is  used. 
In  thermochemical  measurements  it  is  customary  to  employ 
the  calorie  defined  in  (5).  This  is  known  as  the  large  calorie. 
For  measurements  at  room  temperature  the  calorie  defined 


84  THERMAL  MEASUREMENTS. 

in  (4)  is  employed.  For  methods  involving  melting  ice 
(Bunsen's  ice-calorimeter,  etc.)  the  mean  calorie  is  used. 
This  is  the  one-hundredth  part  of  the  heat  necessary  to  raise 
1  gram  of  water  from  0°  C.  to  100°  C.  The  mean  calorie  and 
the  calorie  at  18°  do  not  differ  more  than  one  per  cent,  at 
most.  The  proposition  has  been  made  to  adopt  as  the  unit 
of  quantity  of  heat  4.2  XlO7  ergs,  and  to  call  this  unit  the 
joule,  thus  expressing  heat  values  in  terms  of  their  equiva- 
lent energies. 

Specific  Heat.  —  By  the  specific  heat  of  a  body  we  under- 
stand the  number  of  calories  necessary  to  raise  1  gram  of  the 
substance  1°  C.  Since  the  specific  heat  is  found  to  vary  with 
the  temperature,  the  temperature  at  which  a  determination 
of  the  specific  heat  is  made  should  always  be  specified. 

Determination  of  the  Specific  Heat  of  Solids.  —  The 
method  most  usually  employed  is  known  as  the  method  of 
mixtures,  and  consists  in  heating  a  given  mass  of  the  solid  to 
a  definite  temperature,  and  then  immersing  it  in  a  known 
mass  of  water,  the  initial  and  final  temperatures  of  which  are 
observed.  The  vessel  containing  the  known  mass  of  water 
is  called  a  calorimeter. 

Let  W  =  weight  in  grams  of  solid  of  which  the  specific 

heat  is  to  be  measured; 
T  =  temperature  to  which  the  solid  is  raised; 
C  =  specific  heat  of  the  solid  ; 
w==  weight  of  water  in  calorimeter; 
£  =  initial  temperature  of  water  in  calorimeter; 
6  =  final  temperature  of  water  in  calorimeter. 
Then  we  have 

CW(T-6)=w(6-t), 
or 


c 

0 


W(T-0) 


CALORIMETRY. 


85 


The  calorimeter,  the  stirrer,  and  the  thermometer,  however, 
take  up  a  portion  of  the  heat  lost  by  the  solid,  and  conse- 
quently equation  (1)  must  be  corrected. 

If  the  mass  of  the  calorimeter  be  M,  and  the  specific  heat 
of  the  material  of  which  it  is  made  be  S,  then  MS  is  its 
so-called  water  equivalent: 

In  the  same  manner  the  water  equivalents  of  the  ther- 
mometer and  stirrer  may  be  found  by  multiplying  their 
respective  masses  m  and  m'  by  their  specific  heats  s  and  s'. 
Equation  (1)  then  becomes 


C= 


(w  +  MS +  ms  +  m  V)  (d  - 1) 
W(T-d) 


.     .     (2) 


Heating-vessel. — If  it  is  not  desired  to  heat  the  substance 
higher  than  100°,  the  form  of  apparatus  shown  in  Fig.  39  is 


FIG.  39. 

very  convenient.  The  steam  is  passed  in  and  out  by  means 
of  the  india-rubber  tubes  A  and  B,  and  thus  the  solid  which 
is  placed  in  C  is  heated  to  100°.  This  inner  tube  is  closed 
during  the  heating  by  a  stopper  carrying  the  thermometer. 
A  short-necked  retort  of  copper  in  which  nitrobenzene, 
diphenylamine,  etc.,  may  be  kept  boiling  is  frequently  of 


86  THERMAL  MEASUREMENTS. 

value.  A  stopper  placed  in  the  neck  of  this  retort  carries 
a  test-tube  in  which  the  substance  to  be  heated  is  placed, 
and  also  an  exit-tube  for  the  vapor  of  the  heating  agent. 
The  heating  device  should  be  as  far  away  from  the  calorim- 
eter as  possible,  and  if  it  is  necessary  to  have  it  close  at 
hand  the  calorimeter  must  be  screened  by  means  of  asbestos 
board. 

The  substance,  especially  if  it  be  a  poor  conductor  of 
heat,  is  used  in  small  pieces.  It  is  weighed  in  a  weighing- 
tube,  and  after  introducing  it  into  the  heater  the  tube  is 
reweighed  and  thus  the  weight  of  substance  used  ascer- 
tained. 

The  Calorimeter. — The  calorimeter  consists  of  a  thin- 
walled  cylindrical  metallic  vessel  of  at  least  500  c.c.  capacity. 
It  is  preferable  to  have  the  calorimeter  made  of  platinum 
on  account  of  its  permanence  and  small  heat  capacity,  but 
the  expense  frequently  prohibits  its  employment.  Perhaps 
the  best  substitute  is  nickel,  which  may  be  used  with  water 
and  neutral  or  alkaline  solutions.  A  calorimeter  made  of 
silver  and  gold-plated  on  the  inside  is  also  a  good  substitute 
for  one  of  platinum. 

To  prevent  loss  of  heat  to  surrounding  bodies  the  calorim- 
eter is  placed  in  a  slightly  larger  polished  brass  vessel  of 
cylindrical  section.  The  calorimeter  rests  upon  three  pieces 
of  cork,  which  serve  to  insulate  it  from  the  bottom  of  the 
containing  vessel. 

This  brass  vessel  in  turn  is  placed  coaxially  inside  a 
larger  double-walled  brass  vessel.  The  space  between  the 
walls  is  filled  with  water,  and  the  annular  space  between  the 
double-walled  vessel  and  the  polished  brass  vessel  is  about 
5  cm. 

The  calorimeter  is  provided  with  a  cover,  which  should 
be  made  of  some  poor  conductor.  The  stirrer  is  one  of  the 


CALOR1METRY. 


87 


most  important  parts  of  the  calorimeter,  since  it  is  essential 
that  all  parts  of  the  liquid  shall  be  at  the  same  temperature. 
Many  forms  of  stirrer  have  been  devised,  but  as  efficient  as 
any  is  that  described  by  Ostwald.  It  consists  of  a  circular 
plate  nearly  rilling  the  section  of  the  calorimeter.  In  this 
plate  are  cut  the  necessary  holes  for  the  thermometer  and 
any  other  pieces  of  apparatus,  which  may  be  in  the  interior. 
The  plate  has  H-shaped  openings  cut  in  it,  the  two 


FIG.  40. 

flanges  being  bent  out  of  the  plane  of  the  plate  in  opposite 
directions.  By  means  of  the  flanges  the  stirrer  as  it  is  moved 
up  and  down  gives  to  the  contents  of  the  calorimeter  a 
whirling  motion,  thus  effecting  a  very  complete  mixing. 

If  a  number  of  calorimetric  measurements  are  to  be  made, 
the  stirrer  may  be  operated  mechanically. 

A  cross-section  of  a  calorimeter  is  shown  in  Fig.  40. 
The  thermometer  employed  is  usually  a  Beckmann  instru- 
ment graduated  to  T-i-D-  of  a  degree.  The  specific  heats  of 
the  metals  most  frequently  used  in  the  construction  of  calo- 
rimeters are  here  given: 


88  THERMAL  MEASUREMENTS. 

Platinum 0 . 032 

Silver 0.057 

Nickel 0.110 

Brass 0.094 

Under  no  circumstances  should  glass  be  used  in  the 
construction  of  a  calorimeter. 

Method  of  Operation. — The  substance  of  which  the  spe- 
cific heat  is  to  be  determined  is  placed  in  the  heater  and 
allowed  to  acquire  the  temperature  of  the  vapor  of  the  boil- 
ing water.  The  initial  temperature  of  the  liquid  in  the  calo- 
rimeter is  carefully  noted.  When  the  substance  has  acquired 
the  desired  temperature  it  is  transferred  to  the  calorimeter, 
precautions  being  taken  to  avoid  loss  of  heat  by  radiation. 

The  liquid  in  the  calorimeter  is  stirred  constantly,  care 
being  taken  that  none  of  the  substance  is  removed  by  the 
stirrer  from  the  liquid. 

The  thermometer  is  read  as  directed  below,  and  the  final 
reading  taken.  The  process  is  theoretically  a  simple  one, 
but  practically  it  is  fraught  with  difficulties.  These  diffi- 
culties are:  (1)  loss  of  heat  by  radiation;  (2)  loss  of  heat  to 
the  calorimeter;  (3)  loss  of  heat  to  the  stirrer;  and  (4)  loss 
of  heat  to  the  thermometer.  The  corrections  to  be  applied 
for  each  of  these  losses  will  be  considered  in  the  order  given. 

(i)  Loss  of  Heat  by  Radiation. — Rumford  proposed  to 
correct  for  this  loss  by  making  a  preliminary  experiment  to 
determine  approximately  the  rise  in  temperature  of  the 
calorimeter  and  then  in  the  final  determination  to  cool  the 
calorimeter  before  the  introduction  of  the  heated  substance 
to  a  temperature  below  that  of  the  surrounding  air  by  an 
amount  equal  to  one-half  of  the  rise.  In  this  way  the  calo- 
rimeter would  receive  heat  during  the  first  half  of  the  experi- 
ment and  give  out  heat  during  the  second  half.  Since  the 
temperature  rises  most  rapidly  at  the  beginning,  this  method 


CALORIMETRY.  89 

of  correction  is  far  from  satisfactory  and  for  all  accurate 
work  the  method  of  Regnault  is  employed. 

(1)  First  Period. — Before  the  investigation  is  com- 
menced the  temperature  of  the  calorimeter  is  noted  every 
minute  for  ten  minutes.  Assume  these  temperatures  to  be 
t0,  t1}  t3, .  .  .  tlo.  If  the  experiment  begins  when  tw  is  noted, 
tw  cannot  be  determined  directly,  but  it  is  found  thus: 

L-L 


9 

That  is  to  say,  £10  is  equal  to  £9  plus  the  average  rate  of  change 
of  temperature  during  nine  minutes. 

(2)  Second  Period. — The  beginning  of  this  period  is  simul- 
taneous  with   the   commencement   of   the   experiment.     At 
first  a  rise  in  temperature  is  noted,  then  a  maximum  is 
reached,  after  which  the  temperature  falls.     This  period  is 
assumed  to  continue  for  ten  minutes,  since  after  that  interval 
of  time  the  decrements  of  temperature  are  equal. 

For  this  period  we  have  tlf)  =  r0  at  the  beginning,  and 
Ti>  T2>  T3>  •  •  •  Tio7  the  temperatures  noted  each  minute  during 
the  period. 

(3)  Third   Period. — During    this    period    the    change    in 
temperature  due  to  radiation  is  uniform.     The  temperatures 
observed  at  intervals  of  one  minute  are  TIO  =  #O  and  Olt  62, 
08, .  .  .  010. 

Let  the  temperature  changes  during  the  first,  second, 
and  third  periods  be  denoted  by  J*,  Jr,  and  A8. 

The  average  temperature  changes  for  the  first  and  third 
periods  correspond  to  the  average  temperatures  t5  and  05  of 
these  periods,  or 

,,    t0-tlo  AB    fl0-fl10 

A  ?.  —     _  „       and.     A  K.  —  — 


Now  it  may  be  assumed  that  the  differences  in  the  tem- 
perature changes  are  proportional  to  the  differences  in  the 


90  THERMAL  MEASUREMENTS. 

corresponding   temperatures.     Let    rn   and   An  denote   any 
given  values  for  the  second  period,  then  we  have 


or 


If  we  substitute  for  rn  the  average  of  the  temperature  noted 
at  the  beginning  and  the  end  of  the  nth  minute,  and  for  n  all 
the  values  of  n  from  n  =  0  to  n  =  10,  the  loss  of  heat  due  to 
radiation  for  each  of  the  ten  minutes  of  the  second  period  is 
obtained.  If  now  to  the  final  temperature  TIO  we  add  the 
sum  of  these  differences,  we  obtain  TIO  +  I  A  as  the  corrected 
final  temperature. 

The  calculation  is  performed  thus: 


T3+  .  .  .  T+  '°  _ 


The  method  of  correction  is  best  illustrated  by  an  exam 
ple:* 


Time. 
0.20" 
1.20 
2.20 
3.20 
4.20 
5.20 
6.20 
7.20 
8.20 
Therefore 


Room 

temperature=  23°.5. 

Temp. 

Time. 

Temp. 

19°.  78 

9.20" 

24°.  22 

19  .80 

10.20 

24  .22 

19  .82 

11.20 

24  .22 

19  .84 

12.20 

24  .215 

ling  of 

Expt.            13.20 

24  .215 

23  .54 

14.20 

24  .210 

24  .10 

15.20 

24  .207 

24  .19 

16.20 

24  .204 

24  .21 

17.20 

24  .200 

I  J=  ^23.54+  24.10  +  24.19  +  24.21  +  24.22+  24.22+  24.22+  24.215 

I  94  911  I   19'86+24-21      invlQP'A   (    °-003  +  Q-02\ 
~2~~  9      /  V24.205-19.82/ 


or 


*  Wiillner,  Physik,  3,  p.  407. 


CALORIMETRY. 


91 


This  correction  has  then  to  be  added  to  the  temperature 
observed  at  the  end  of  the  second  period,  or  TIO  =  24.210,  or 

24.210+ 0.015  =  24°.225. 

Another  method  for  correcting  for  loss  of  heat  due  to 
radiation  is  to  read  the  temperature  of  the  calorimeter  at 
short  intervals  of  time,  r,  after  introducing  the  heated  body 
until  the  maximum  temperature  has  been  reached.  The 
fall  of  temperature  in  two  or  three  minutes  is  then  deter- 


TEMPERATURE  OF  CALORIMETER 

FIG.  41. 


mined,  and  from  this  the  fall  in  the  interval  T  calculated.  In 
this  way  we  ascertain  the  rate  of  cooling  at  the  maximum 
temperature. 

The  rate  of  cooling  is  then  determined  at  a  number  of 
temperatures  between  the  maximum  and  the  initial  temper- 
atures. A  curve  PQ  is  then  drawn  (Fig.  41)  in  which  the 
temperatures  of  the  calorimeter  are  plotted  as  abscissae, 
while  the  fall  in  temperature  at  the  different  temperatures 
during  the  interval  r  are  plotted  as  ordinates. 

The  readings  of  the  thermometer  in  the  calorimeter  while 
the  thermometer  was  rising  are  plotted  against  times  from 
the  instant  when  the  heated  body  was  introduced.  This 


92 


THERMAL  MEASUREMENTS. 


curve  will  have  the  form  shown  by  (Fig.  42)  the  continuous 
line  DEC. 

From  a  point  N,  which  corresponds  to  a  time  interval  ~, 

2t 

the  ordinate  NR  is  drawn.  The  temperature  corresponding 
to  R  is  then  read  from  the  axis  of  ordinates.  From  the 
curve  in  Fig.  43,  the  fall  of  temperature  during  the  time  r 
when  the  calorimeter  was  at  the  temperature  corresponding 
to  R  in  Fig.  42  is  then  read  off.  This  quantity  is  then  added 


to  the  ordinate  MD,  giving  a  new  point,  D1 ',  which  represents 
what  the  temperature  of  the  calorimeter  would  have  been 
had  there  been  no  loss  by  radiation.  In  a  similar  manner 
the  points  E',  B',  etc.,  are  obtained.  From  E'  the  curve 
remains  horizontal,  since  if  there  had  been  no  loss  by  radia- 
tion when  the  heated  body  and  calorimeter  had  reached  the 
same  temperature,  the  temperature  would  have  remained 
constant.  The  temperature  corresponding  to  E'  would 
therefore  be  the  "  corrected  temper ature." 

(2)  Loss  of  Heat  to  Calorimeter. — The  water  equivalent 
of  the  calorimeter  is  obtained  by  multiplying  the  weight  of 


CALORIMETRY.  93 

the  vessel  by  the  specific  heat  of  the  material  of  which 
it  is  made.  The  table  of  specific  heats  on  p.  82  will  give 
the  necessary  data  for  such  calorimeters  as  are  usually 
employed. 

(3)  Loss  of   Heat   to    Stirrer. — The  water  equivalent  of 
the  stirrer  is  calculated  in  the  same  manner  as  that  of  the 
calorimeter.     It  should  be  noted,  however,  that  only  that 
portion  of  the  stirrer  which  is  immersed  should  be  taken  into 
account. 

(4)  Loss  of  Heat  to  the  Thermometer. — The   calculation 
of  the  water  equivalent  of  the  thermometer  is  complicated  by 
the  uncertainty  as  to  the  weights  of   the  glass  and  mercury 
separately. 

Fortunately,  however,  the  heat  capacities  of  glass  and 
mercury  for  equal  volumes  are  nearly  equal.  The  specific 
.heat  of  mercury  =  0.034,  and  its  density  =13. 56.  Its  heat 
capacity  =  0.034X13.56  =  0.46  per  c.c.  The  specific  heat  of 
glass  =  0.19,  and  its  density  =  2.4.  Its  heat  capacity  =  0. 19 X 
2.4  =  0.46  per  c.c. 

It  is  therefore  only  necessary  to  measure  the  volume  of 
the  bulb  of  the  thermometer  and  multiply  by  0.46  in  order 
to  obtain  the  water  equivalent. 

The  determination  of  the  volume  is  most  easily  made  by 
weighing  to  centigrams  a  beaker  partially  filled  with  water, 
and  then  suspending  in  it  the  thermometer  with  the  bulb 
immersed  and  observing  the  increase  in  weight  of  the 
beaker. 

Determination  of  the  Specific  Heat  of  Liquids. — Probably 
the  most  accurate  method  for  the  determination  of  the  spe- 
cific heat  of  a  liquid  is  that  due  to  Pfaundler  and  Magie.*  It 
consists  in  the  comparison  of  the  specific  heat  of  a  liquid  in 
one  calorimeter  with  that  of  the  specific  heat  of  another 

*  Magie,  Phys.  Rev.,  Vol.  IX,  No.  2,  p.  65. 


94  THERMAL  MEASUREMENTS. 

liquid  chosen  as  a  standard  in  another  calorimeter.  This 
comparison  is  made  by  observing  the  increase  of  tempera- 
ture produced  in  each  calorimeter  when  equal  quantities  of 
heat  are  supplied.  These  equal  quantities  of  heat  are  pro- 
duced by  passing  an  electric  current  through  two  coils  of 
the  same  resistance  connected  in  series,  each  calorimeter 
being  provided  with  one  coil.  By  so  proportioning  the  quan- 
tities of  the  liquids  that  the  rise  in  temperature  is  identical  in 
each  calorimeter  the  usual  calorimetric  corrections  may  be 
neglected. 

A  section  of  one  of  the  calorimeters  is  shown  in  Fig.  43. 
It  consists  of  a  cylindrical  cup  of  thin  brass  four  inches  in 
diameter  and  six  inches  high.  It  is  placed  within  a  larger 
brass  vessel  six  inches  in  diameter  and  eight  inches  high,  and 
is  centred  by  means  of  wooden  pins  projecting  from  the 
inner  walls  of  the  outer  vessel.  Through  the  wooden  covei 
of  the  calorimeter  pass  two  heavy  copper  wires,  which  are 
connected  below  the  surface  of  the  liquid  by  a  German-silver 
resistance  of  nearly  4  ohms.  The  coil  is  held  in  position  by 
a  glass  rod  which  projects  downward  from  the  cover.  The 
heavy  copper  wires  and  the  German-silver  spiral  are  insu- 
lated by  means  of  a  varnish  which  resists  the  action  of 
liquids.  By  means  of  a  hot-air  motor  or  a  turbine  the 
stirrers  of  the  two  calorimeters  are  operated,  since  inequal- 
ity in  stirring  produces  an  appreciable  error.  The  thermome- 
ter is  inserted  as  shown,  the  bulb  being  about  an  inch  below 
the  surface  of  the  liquid.  The  current  for  the  coils  is  fur- 
nished by  a  dynamo  or  storage-cells,  the  circuit  including  a 
contact-maker,  an  ammeter,  and  a  variable  resistance. 
The  current  used  should  range  from  4  to  5  amperes. 

Method  of  Operation. — One  calorimeter  is  filled  with  the 
standard  liquid,  usually  500  or  600  grams  of  water.  The 
other  calorimeter  is  filled  with  enough  of  the  liquid  of  which 


CALORIMETRY.  95 

the  specific  heat  is  sought  to  give  an  equal  rise  in  tempera- 
ture. This  must  be  determined  by  preliminary  trials.  The 
two  calorimeters  are  cooled  a  few  degrees  below  room  tem- 


FIG.  43. 

perature,  and  then  placed  in  their  respective  positions  and 
stirred.  If  the  temperatures  are  not  the  same,  the  cooler 
vessel  may  be  warmed  with  the  hands.  When  the  two  cups 


96  THERMAL  MEASUREMENTS. 

are  within  a  few  tenths  of  a  degree  of  equality  of  tempera- 
ture the  current  is  switched  on  and  the  stirring  started. 
The  current  is  turned  off  when  the  temperature  has  risen  as 
much  above  that  of  the  room  as  it  was  below  at  the  begin- 
ning of  the  experiment.  The  stirring  is  now  continued  and 
the  thermometer  observed  until  the  maximum  temperature 
is  reached. 

Let  <91  =  rise  of  temperature  in  water; 
02=  "    "  "  "  liquid; 

m1  =  mass  of  water; 
m2=    "      "  liquid; 

s  =  specific  heat  of  liquid. 
Then  we  have 


or 


mn 


For  further  details  the  student  should  consult  the  orig- 
inal papers  of  Prof.  Magie  in  the  Physical  Review,  Vols.  IX, 
XIV,  and  XVI. 

Heat  of  Fusion. — The  heat  of  fusion  of  a  substance  is 
the  quantity  of  heat  required  to  convert  one  gram  of  the 
substance  from  the  solid  to  the  liquid  state  without  chang- 
ing its  temperature. 

The  molecular  heat  of  fusion  is  the  product  of  the  molec- 
ular weight  of  the  substance  and  the  heat  of  fusion.  The 
heat  of  solidification  of  a  substance  is  the  quantity  of  heat 
liberated  when  one  gram  of  the  substance  is  changed  from 
the  liquid  to  the  solid  state. 

The  molecular  heat  of  solidification  is  the  product  of  the 
molecular  weight  of  the  substance  and  the  heat  of  solidifi- 
cation. 


CALORIMETRY.  97 

Since  substances  after  solidifying  are  not  always  in  the 
same  molecular  condition,  there  are  often  considerable  dif- 
ferences between  the  heats  of  fusion  and  solidification. 
Whenever  possible  it  is  preferable  to  determine  the  heat  of 
fusion  rather  than  the  heat  of  solidification. 

The  method  usually  employed  is  Regnault's  method  of 
mixtures  (p.  78). 

(1)  Heat  of  Fusion. — If  the  substance  melts  below  the 
temperature  of  the  room,  it  is  introduced  into  the  calo- 
rimeter in  the  solid  state  and  allowed  to  melt.  The  calo- 
rimeter is  provided  with  enough  liquid  so  that  the  final 
temperature  shall  be  above  that  of  the  melting-point  of  the 
substance. 

The  total  quantity  of  heat  lost  by  the  liquid  in  the  calo- 
rimeter is  the  sum  of  three  quantities,  as  follows: 

(1)  The  quantity  of  heat  taken  up  by  the  substance  in 
passing  from  the  initial  temperature  of  the  liquid  in  the 
calorimeter  to  that  of  the  melting-point  of  the  substance. 

(2)  The  quantity  of  heat  required  to  melt  the  substance. 

(3)  The  quantity  of  heat  required  to  heat  the  melted 
substance  to  the  final  temperature  of  the  liquid  hi  the  calo- 
rimeter. 

Let  L  =  heat  of  fusion  of  the  substance; 

T  =  temperature  of  substance  when  introduced  into 

calorimeter; 
M  =  mass  of  substance ; 
S  =  specific  heat  of  solid  substance; 
Si  =  specific  heat  of  liquid  substance ; 
ra  =  mass  of  liquid  in  calorimeter  (usually  water) ; 
s  =  specific  heat  of  liquid  in  calorimeter  (for  water  = 

i); 

tj_  =  initial  temperature  of  liquid  in  calorimeter; 
£0  =  melting  temperature  of  substance; 


98  THERMAL  MEASUREMENTS. 

t2  =  final  temperature  of  liquid  in  calorimeter; 

wl  =  water  equivalent  of  vessel  containing  substance; 

w2  =  water  equivalent  of  calorimeter  and  accessories. 
Then  the  quantity  of  heat  given  up  by  the  calorimeter  and 
its  contents  will  be  (m-f  w2)(^  —  Q,  and  the  quantity  of  heat 
absorbed  b    the  substance  and  vessel  will  be 


Equating  these  two  expressions  and  solving  for  L,  we  get 
,     (m  +  to,)  (t,  -  Q  -to,  fe  -  D  -  M[S(tt  -  T)  +  S,(t,  -  f  .)] 

~W~ 

(2)  Heat  of  Solidification.  —  Shoulcl  the  melting-point  of 
the  substance  be  above  that  of  the  temperature  of  the  room, 
then  the  heat  of  solidification  is  obtained. 

A  moment  's  reflection  will  make  it  clear  that  the  method 
is  exactly  the  reverse  of  that  given  above.  Denoting  the 
heat  of  solidification  by  E,  the  formula  for  this  quantity  can 
be  shown  to  be 


Method  of  Operation.  —  The  substance  in  either  the  solid 
or  the  liquid  state  is  introduced  into  the  calorimeter  in  a 
small  platinum  or  silver  bottle. 

The  specific  heats  of  the  solid  and  liquid  substances  are 
ascertained  for  the  interval  of  temperature  of  the  experi- 
ment. The  experimental  details  are  exactly  similar  to 
those  in  the  determination  of  specific  heat  (p.  88). 

The  heat  of  fusion  may  be  calculated  approximately 
from  the  molecular  depression  of  the  freezing-point  for  the 
substance  as  a  solvent. 

If  L  is  the  heat  of  fusion  of  the  solvent,  T  its  freezing- 


CALORlMETRY.  99 

point  in  absolute  temperature,  and  J  its  molecular  depression, 

then 

7     0.02772 
~T~ 

Heat  of  Vaporization.  —  The  heat  of  vaporization  is  the 
quantity  of  heat  required  to  convert  one  gram  of  a  liquid  at 
its  boiling-point  into  vapor  at  the  same  temperature. 

The  molecular  heat  of  vaporization  is  the  product  of  the 
molecular  weight  of  the  substance  and  the  heat  of  vaporiza- 
tion. There  is  no  difference  in  value  between  the  heat  of 
vaporization  and  the  heat  of  condensation. 

The  method  employed  in  the  measurement  of  this  quan- 
tity consists  in  vaporizing  a  definite  quantity  of  liquid  and 
condensing  the  vapor  in  a  calorimeter. 
Let  V  =  heat  of  vaporization  ; 

M  =  mass  of  liquid  converted  into  vapor  ; 
T  =  boiling-point  of  liquid; 
<2  =  final  temperature  of  water  in  calorimeter  ; 
/S  =  mean  specific  heat  of  liquid  between  T  and  t2; 
m  =  mass  of  water  in  calorimeter; 
w  =  water  equivalent  of  calorimeter  and  accessories; 
2,  =  initial  temperature  of  water  in  calorimeter. 
Then  the  quantity  of  heat  given  up  by  the  vapor  in  con- 
densing to  a  liquid  in  the  calorimeter  is  M[S(T  —  t2)  -f  T7],  and 
the  quantity  of  heat  taken  up  by  the  calorimeter  and  con- 
tents is  (m  +  w)(t2  —  t.). 

Equating  these  two  expressions  and  solving  for  V,  we 
have 

(m  +  w)(tt-t;)-MS(T-t,) 
M 

Apparatus  and  Method.  —  The  method  here  described  is 
Kahlenberg's  modification  of  Berthelot's  method.*  The 


*  Kahlenberg,  Jour  Phys.  Chem    VoJ  5  No  4,  p.~215 


100 


THERMAL  MEASUREMENTS. 


main  difference  between  this  new  apparatus  and  that  d  - 
vised  by  Berthelot  lies  in  the  construction  of  the  retort. 
The  construction  of  the  apparatus  is  shown  in  Fig.  44,  the 


Fro:  44. 

retort  being  represented  rather  large  in  proportion  to  the 
rest  of  the  apparatus  in  order  to  show  the  details.  The 
retort  where  the  liquid  is  heated  consists  of  a  test-tube  17  cm. 


CALOR1METRY.  101 

long  and  3.5  cm.  in  diameter,  into  the  bottom  of  which  is 
fused  the  tube  a,  which  fits  into  the  condenser  with  a  ground- 
glass  joint  at  b.  At  c  there  are  two  large  lateral  openings. 
The  glass  tubes  e  and  /  pass  through  a  good  cork,  d.  Into 
these  tubes  are  fused  the  ends  of  the  spiral  of  platinum  wire 
g.  This  spiral  consists  of  about  40  cm.  of  stout  platinum 
wire,  to  the  ends  of  which  are  welded  short  heavy  pieces  of 
platinum  rod;  and  these  rods  in  turn  are  fused  into  the 
glass  tubes.  Long,  rather  heavy  copper  wires  pass  down 
the  glass  tubes  at  the  bottom  of  which  they  are  connected 
with  the  ends  of  the  platinum  rods  by  means  of  a  few  drops 
of  mercury.  Two  small  binding-screws  serve  to  connect 
the  copper  wires  with  the  ends  of  other  wires  that  lead  to  the 
source  of  electricity,  as  indicated  in  the  illustration. 

It  is  obviously  essential  that  the  lower  end  of  the  tube  of 
the  retort  which  connects  with  the  condenser  at  6  be  made  so 
short  as  to  prevent  premature  condensation  of  the  vapors 
in  this  part  of  the  tube.  In  the  figure  this  protruding  part 
of  the  tube  has  been  represented  rather  longer  relatively 
than  it  ought  to  be. 

The  calorimeter  is  covered  with  a  heavy  piece  of  asbestos 
board  coated  with  tin-foil  and  shaped  so  as  to  fit  snugly. 
The  small  space  between  the  bottom  of  the  retort  and  the 
cover  of  the  calorimeter  is  nicely  packed  with  cotton,  and  in 
fact  the  whole  retort  is  inclosed  in  cotton  during  the  prog- 
ress of  the  experiment,  a  few  peep-holes  being  left  through 
which  the  boiling  may  be  observed.  This  cotton  covering 
of  the  retort  which  has  not  been  represented  in  the  figure 
serves  very  effectively  to  screen  the  thermometer  and  calo- 
rimeter from  the  hot  retort ;  at  the  same  time  it  prevents  the 
latter  from  becoming  chilled,  thus  materially  aiding  the 
progress  of  the  experiment.  This  screen  can  be  made  very 
easily  by  gluing  a  layer  of  cotton  batting  on  thin  asbestos 


102  THERMAL  MEASUREMENTS. 

paper.  By  placing  the  screen  so  as  to  rest  on  the  calorimeter- 
cover  it  may  be  bent  so  as  to  inclose  the  retort,  remaining 
in  position  without  any  further  support.  The  calorimeter,  of 
about  1250  c.c.  capacity,  is  made  of  very  thin  nickel-plated 
sheet  copper.  It  is  somewhat  elliptical  in  shape,  thus  per- 
mitting the  thermometer  to  be  placed  at  a  greater  distance 
from  the  retort  than  would  be  possible  by  using  a  vessel  of 
the  same  capacity  but  of  circular  cross-section.  The  stirrer, 
which  is  not  represented  in  the  figure,  is  made  of  thin  copper: 
It  is  provided  with  a  hard-rubber  handle,  by  means  of  which 
an  up-and-down  motion  is  imparted  to  it.  The  thermometer 
employed  is  of  the  Beckmann  type.  The  condenser  is  made 
of  glass.  A  current  of  from  8  to  15  amperes,  according  to 
the  nature  of  the  liquid  under  investigation,  is  sufficient  to 
heat  the  liquid  to  boiling. 

This  current  is  taken  either  from  a  dynamo  or  from 
twelve  or  more  large  storage-cells,  representing  an  E.M.F.  of 
about  24  volts.  A  rheostat  placed  in  the  circuit  permits 
the  current  to  be  adjusted  as  desired,  the  strength  of  the 
latter  being  indicated  by  an  ammeter. 

The  liquids  are  brought  to  boiling  rather  slowly,  but 
are  kept  boiling  vigorously  when  once  ebullition  has  started. 
The  boiling  is  usually  continued  for  about  five  minutes,  care 
being  taken  not  to  evaporate  the  liquids  so  far  as  to  expose 
the  platinum  spiral.  The  amount  of  liquid  evaporated  is 
ascertained  by  weighing  both  the  retort  and  condenser  on 
an  analytical  balance  before  and  after  the  experiment.  The 
weights  thus  obtained  act  as  a  check  upon  each  other;  they 
generally  agree  to  within  a  few  centigrams.  The  average  of 
these  two  weights  is  taken.  The  loss  of  heat  due  to  radiation 
during  the  experiment  is  corrected  by  the  method  of  Reg- 
nault-Pfaundler  given  on  p.  94. 

In  Fig.  45  is  shown  a  simpler  form  of  retort,  also  devised 


CALOR1METRY. 


103 


by  Kahlenberg.  Here  the  test-tube  is  inverted,  the  lower 
end  being  closed  with  a  good  rubber  stopper,  through  which 
the  glass  tube  passes,  connecting  with  the  condenser  as  indi- 
cated. The  ends  of  the  spiral  of  platinum  wire  are  welded 
to  rather  heavy  platinum  rods,  which  pass  through  the 
rubber  stopper  as  shown  in  the  figure.  The  ends  of  these 
rods  are  connected  with  the -wires  leading  to  the  source  of 


FIG.  45. 

electricity  by  means  of  small  binding-screws.  This  form  of 
the  retort  is  much  simpler  than  that  in  Fig.  40,  and  it  is  con- 
sequently to  be  preferred  whenever  the  liquid  tested  does 
not  attack  the  rubber  stopper.  Rubber  being  a  poor  con- 
ductor of  heat,  the  stopper  itself  serves  to  screen  the  calo- 
rimeter from  the  hot  liquid  in  the  retort.  The  heat  of 
vaporization  may  also  be  calculated  from  the  elevation  of 


104  THERMAL  MEASUREMENTS. 

the  boiling-point  in  the  same  manner  as  the  heat  of  fusion 
is  calculated  from  the  depression  of  the  freezing-point. 
The  formula  is 

0.02T2 

~7~; 

where  V  is  the  heat  of  vaporization,  T  the  absolute  tem- 
perature at  which  the  liquid  boils,  and  p  is  the  molecular 
elevation  of  the  boiling-point  for  the  liquid  as  a  solvent. 

A  very  interesting  relation  between  molecular  heats  of 
vaporization  and  absolute  boiling  temperatures  has  been 
pointed  out  by  Trouton.  This  rule  states  that  the  molecular 
heats  of  vaporization  are  proportional  to  the  absolute  tempera- 
tures at  which  the  liquids  boil.  This  may  be  formulated  thus: 

^rr  =  const  ant. 

That  it  certainly  holds  for  a  large  variety  of  substances  has 
been  shown  by  Ostwald  and  others.* 

Thermochemistry.  --In  all  thermochemical  measure- 
ments it  is  found  convenient  to  employ  as  a  unit  the  large 
calorie,  which  is  one  hundred  times  the  small  calorie.  The 
large  calorie,  then,  is  nearly  equal  to  the  quantity  of  heat 
required  to  raise  1  gram  of  water  from  0°  to  100°. 

The  results  of  thermochemical  measurements  are  always 
expressed  in  terms  of  gram-molecular  weights. 

The  notation  employed  is  that  due  to  J.  Thomsen. 

The  following  examples  will  serve  to  illustrate  the  method 
of  expressing  the  results: 

H2+0=H20  +  68,360  cals., 
or 

[H2,0]  =  68,360+. 

*Phil.  Mag.,  18,  54  (1884);  Liebig's  Ann.,  234,  338  (1886);  Ost- 
wald's  Lehrbuch  d.  allg.  Chem.,  1,  335. 


CALORIMETRY.  105 

Either  of  these  equations  means  that  when  2  grams  of  hydro- 
gen unite  with  1  gram  of  oxygen  to  form  18  grams  of  water 
68,360  calories  of  heat  are  set  free. 
In  the  same  manner 

NH3+HC1=NH4C1+41,900  cals., 
or 

[NHS,  HC1]  =  41,900+, 

expresses  that  41,900  calories  of  heat  are  liberated  when 
one  gram-molecule  of  ammonium  chloride  is  formed  from 
one  gram-molecule  of  ammonia  and  one  gram-molecule  of 
hydrochloric  acid. 

The  plus  sign  shows  that  the  reaction  is  exothermic. 
Should  the  reaction  be  endothermic,  a  minus  sign 'would 
express  the  fact. 

If  the  reaction  takes  place  in  the  presence  of  a  large 
quantity  of  water,  the  equation  is  written 

KOH  aq.  +  HCl  aq.=KCl  aq.  + 13,700  cals., 

where  the  symbol  aq.  shows  that  the  potassium  hydroxide, 
the  hydrochloric  acid,  and  the  potassium  chloride  are  each 
in  solution. 

If  it  is  desired  to  represent  the  heat  liberated  when  a 
substance  dissolves  in  water,  the  symbol  aq.  is  written  after 
the  formula  of  the  substance,  thus: 

HC1,  aq.  =  17,320. 

This  means  that  when  one  gram-molecule  of  hydrochloric 
acid  dissolves  in  water  17,320  calories  of  heat  are  set  free. 

If  both  chemical  action  and  solution  are  to  be  repre- 
sented, the  equation  is  written 

H+  Cl  +  aq.  =  HC1  +  aq.  +  39,300. 


106  THERMAL  MEASUREMENTS. 

This  expressed  in  words  is  that  when  one  gram-molecule  of 
hydrogen  combines  with  thirty-five  and  four-tenths  grams 
of  chlorine  in  the  presence  of  water  the  heat  liberated  due 
to  combination  and  solution  is  39,300  calories. 

The  state  of  aggregation  of  the  reacting  substances  and  of 
the  resulting  products  is  commonly  expressed  by  means  of  the 
type.  The  gaseous  state  is  represented  by  italics,  the  liquid 
by  ordinary  type,  and  the  solid  by  extra-heavy  type,  thus: 

H20 water  vapor 

H20 liquid  water 

H»O ice. 

The  most  important  of  the  thermochemical  laws  are: 

(1)  Law  of  Lavoisier  and  Laplace. — The  amount  of  heat 
which  is  required  to  decompose  a  compound  into  its  con- 
stituents is  exactly  equal  to  that  which  was  evolved  when 
the  compound  was  formed  from  these  constituents. 

(2)  Laws  of  Hess. — (a)  The  heat  evolved  in  a  chemical 
process  is  the  same  whether  it  takes  place  in  one  or  in  sev- 
eral steps. 

(6)  If  two  salt  solutions  which  are  nearly  completely 
dissociated  are  mixed,  no  thermal  change  occurs,  provided 
the  ions  do  not  unite  to  form  molecules. 

(3)  Laws   of  Berthelot. — (a)  The    thermal    change   in    a 
chemical  reaction,  if  no  work  is  done,  depends  only  upon  the 
condition  of  the  system  at  the  beginning  and  at  the  end 
of  the  reaction,  and  not  on  the  intermediate  conditions. 

(6)  The  heat  evolved  in  a  chemical  process  is  a  measure 
of  the  corresponding  chemical  and  physical  work. 

(c)  Every  chemical  transformation  which  takes  place 
without  the  addition  of  energy  from  without,  tends  to  form 
that  substance  or  system  of  substances,  the  production  of 


CALORIMETRY. 


107 


which  is  accompanied  by  the  evolution  of  the  maximum 
amount  of  heat. 

For  a  discussion  of  these  laws  and  a  fuller  treatment  of 
the  subject  of  thermochemistry  the  student  must  consult 
a  text-book  of  physical  chemistry. 

Heat  of  Neutralization. — When  an  acid  is  neutralized  by 
a  base  heat  is  set  free.  The  amount  of  heat  liberated  when 
one  gram-molecule  of  an  acid  reacts  with  one  gram-molecule 
of  a  base,  in  dilute  solution,  is  called  the  heat  of  neutraliza- 
tion. 

Apparatus  and  Method  of  Operation.  —  The  apparatus 
used  is  a  modification  of  that  devised  by  Thomsen.  The 
main  points  of  it  are  shown  in  Fig.  46. 


FIG.  46. 

A  and  B  are  two  cylindrical  vessels  having  respective 
capacities  of  1000  and  500  c.c.  The  vessels  may  be  made 
of  nickel-plated  brass.  The  vessel  B  communicates  with  A 
through  the  valve  V,  which  can  be  opened  by  means  of  the 
handle  p. 


4 

108  THERMAL  MEASUREMENTS. 

Both  A  and  B  are  provided  with  stirrers  r  and  R,  and 
with  insulating  covers  which  are  perforated  to  admit  the 
thermometers  and  stirrers.  The  two  vessels  are  provided 
with  outer  cylinders  of  polished  brass  (not  shown  in  figure) 
to  insure  insulation. 

The  thermometers  used  are  of  the  Beckmann  type  grad- 
uated to  ^  or  -j-^  of  a  degree. 

The  thermometers  should  be  compared  frequently  by 
observing  the  temperatures  indicated  by  each  when  im- 
mersed in  the  same  liquid. 

The  rules  already  given  for  the  use  of  a  calorimeter  are 
to  be  applied  in  the  use  of  this  apparatus.  The  solutions 
used  should  be  very  dilute;  usually  one  gram  equivalent  of 
acid  or  base  in  two  hundred  gram-molecules  of  water. 

It  will  be  found  convenient  to  have  an  exact  submultiple 
of  the  molecular  weight  of  the  solution  in  the  calorimeter. 
For  a  solution  of  NaOH+100H20  (molecular  weight  1840 
grams)  one-fourth  or  one-sixth  of  a  gram  molecule  is  used; 
the  solution  would  then  contain  450  or  300  grams  of  water. 

In  the  same  manner  for  an  equivalent  solution  of  sul- 
phuric acid,  JH2S04+100H20,  one-fourth  or  one-sixth 
equivalent  should  be  placed  in  the  calorimeter.  It  is  obvi- 
ously a  matter  of  indifference  which  vessel  contains  the  acid 
and  which  the  base. 

The  solutions  should  be  thoroughly  stirred  and  the 
thermometers  carefully  noted.  When  the  temperatures  have 
remained  constant  for  several  minutes  the  thermometers 
are  read  and  the  valve  V  opened.  The  establishment  of 
thermal  equilibrium  takes  only  a  very  short  time  (usually 
one  minute).  The  measurements  should  be  made  at  room 
temperature  (18°  to  20°).  If  the  change  in  temperature 
after  mixing  is  not  more  than  1°,  no  radiation  correction  need 
be  applied. 


CAWRIMETRY.  109 

Let  Mt=M2  be  the  weights  of  water  in  the  two  solutions; 
tt  be  the  temperature  of  the  solution  in  vessel  con- 

taining Mt  grams  of  water  ; 
t2  be  the  temperature  of  the  solution  in  vessel  con- 

taining M2  grams  of  water; 
6  be  the  final  temperature  after  mixture  ; 
w  be  the  total  water.  equivalent; 

—  be  the  fraction  of  a  gram-molecule  which  is  con- 

tained in  the  solutions  ; 
N  be  the  heat  of  neutralization  for  one  gram-mole- 

cule expressed  in  large  calories. 

Then  we  have 


2 

This  formula  assumes  the  specific  heat  of  the  solutions 
to  be  unity,  which  is  permissible  for  very  dilute  solutions. 

Heat  of  Solution.  —  The  heat  evolved  or  absorbed  by  the 
solution  of  one  gram-molecule  of  a  substance  in  a  definite 
number  of  molecules  of  solvent  is  known  as  the  heat  oj  solu- 
tion. 

Apparatus  and  Method  of  Operation.  —  The  apparatus 
employed  is  the  mixture-calorimeter.  All  of  the  precautions 
which  were  given  under  the  determination  of  specific  heat 
must  be  observed  here. 

It  is  advisable  to  have  a  fractional  part  of  the  molecular 
weight  of  the  solution  in  the  calorimeter,  as  in  determining 
the  heat  of  neutralization. 

—  gram-molecules  of  the  solute  is  weighed  out,  and  M 

iYv 

grams  of  water  are  weighed  in  the  calorimeter.     Denoting  by 
w  the  total  water  equivalent  and  letting  t  and  6  denote  the 


110  THERMAL  MEASUREMENTS. 

initial  and  final  temperatures,  the  heat  of  solution  S  is  given, 
in  large  calories,  by  the  formula 


Here,  as  in  the  formula  for  heat  of  neutralization,  the  specific 
heat  of  the  solution  is  assumed  to  be  unity.  In  order  that 
both  solute  and  solvent  may  acquire  the  common  tem- 
perature t,  the  weighed  quantity  of  solute  is  sealed  in  a  thin 
gla  s  bulb  and  introduced  into  the  water.  When  the  tem- 
perature has  become  uniform  the  bulb  is  broken  by  means 
of  the  stirrer.  The  accuracy  of  the  results  depends  upon 
the  time  required  for  complete  solution. 

Should  the  final  temperature  vary  more  than  three 
degrees  from  that  of  the  room,  the  correction  for  radiation 
must  be  applied. 

The  method  given  above  is  obviously  only  applicable  to 
solids  and  liquids.  To  determine  the  heat  of  solution  of 
gases  the  gas  is  bubbled  through  the  water  in  the  calorimeter, 
the  size  of  the  bubbles  being  regulated  according  to  the 
solubility  of  the  gas.  The  solution  in  the  calorimeter  is 
then  analyzed  and  thus  the  quantity  of  gas  dissolved  is 
determined.  The  arrangement  of  apparatus  for  determining 
the  heat  of  solution  of  a  gas  is  shown  in  Fig.  47.  If  it  is 
desired  to  determine  the  heat  of  solution  of  a  salt  containing 
water  of  crystallization,  care  should  be  taken  to  have  the 
quantity  of  water  in  excess  of  that  present  in  the  salt,  other- 
wise the  salt  will  lose  water  of  crystallization. 

If  the  salt  contains  n  molecules  of  water  of  crystalliza- 
tion, 200  —n  or  400  -n  molecules  of  water  are  chosen  as 
solvent.  Thus,  for  MgS04  +  7H20,  393  molecules  of  water 
would  be  used  as  solvent.  Since  the  heat  of  solution  is 
numerically  equal  to  the  heat  of  precipitation,  the  former 


CALORIMETRY. 


Ill 


may  be  measured  by  the  latter.  To  measure  the  heat  of 
solution  from  the  heat  given  out  in  the  precipitation  of  a 
gram-molecule  of  solute  it  is  necessary  to  (1)  form  the  sub- 
stance in  the  solution  at  such  a  dilution  that  no  precipitation 
occurs,  and  (2)  so  that  precipitation  is  complete.  The  dif- 


FIG.  47. 

fere  nee  between  these  two  heat  values  is  the  heat  of  solution 
sought. 

Heat  of  Hydration. — The  quantity  of  heat  liberated  when 
one  gram-molecule  of  a  salt  combines  with  a  definite  number 
of  molecules  of  water  to  form  a  hydrate  is  known  as  the  heat 
of  hydration. 

The  heat  of  hydration  is  obtained  by  subtracting  the 
heat  of  solution  of  the  hydrated  salt  from  the  heat  of  solution 
of  the  anhydrous  salt. 

The  method  for  the  determination  of  the  heat  of  hydra- 
tion is  thus  that  for  the  heat  of  solution.  If  it  is  desired,  for 
example,  to  obtain  the  heat  of  hydration  when  CaCl2+6H20 
is  formed  from  CaCl2,  we  measure  (1)  heat  of  solution  of 
CaCl2=Sl;  and  (2)  heat  of  solution  of  CaCl2+6H20  =  £2. 


112  THERMAL  MEASUREMENTS. 

The  thermal  effect  in  the  first  process  consists  of  two 
parts:  (a)  the  heat  of  hydration  of  CaCl2  (positive  thermal 
effect),  (6)  the  heat  of  solution  of  CaCl2+6H20  (negative 
thermal  effect). 

The  thermal  effect  in  the  second  process  consists  of  the 
thermal  effect  CaCl2+6H20,  aq.  The  heat  of  hydration  H  is 

H=Sl-S2. 

The  thermal  effects  for  the  combination  with  the  first,  second, 
third,  etc.,  molecules  of  water  are  usually  quite  different. 
For  this  reason  it  is  advisable  to  determine  the  heats  of 
hydration  for  1,  2,  3  ...  n  molecules  of  water  of  crystalliza- 
tion. The  salts  are  dehydrated  in  an  ordinary  drying-oven. 
The  directions  given  on  p.  110  should  be  followed  in  mak- 
ing up  the  solutions. 

Heat  of  Dilution. — The  thermal  change  which  is  caused 
by  the  dilution  of  a  solution  with  the  solvent  is  known  as  the 
heat  of  dilution.  The  quantity  of  water  of  the  solution  and 
the  ultimate  quantity  of  water  are  ordinarily  so  chosen 
that  the  total  quantity  is  a  constant.  Thus  HC1  50  aq.,  50  aq., 
HC1  25  aq.,  75  aq.,  HC1  30  aq.,  70  aq.,  etc.,  or  in  general 
HC1  n  aq.,  100-  n  aq. 

The  heat  of  dilution  is  best  determined  in  the  mixture- 
calorimeter,  the  process  being  nearly  analogous  to  that  for  the 
determination  of  the  heat  of  solution.  The  solution  to  be 
diluted  is  introduced  into  the  calorimeter  in  a  small,  closed 
glass  vial ;  when  the  temperature  has  become  uniform  the  vial 
is  broken  and  the  thermal  change  noted. 

Let  tw  =  ihe  initial  temperature  of  the  water; 
£«  =  the  initial  temperature  of  the  solution; 
6  =  final  temperature  of  the  mixture; 
c  =  specific  heat  of  the  mixture ; 
w  =  water  equivalent  of  calorimeter  and  accessories' 


CALORIMETRY.  113 

of  the  water; 
M«  =  mass  of  the  solution  to  be  diluted; 

— = fraction  of  a  gram-molecule  of  solute  contained 
ra 

in  solution; 

D  =  heat  of  dilution. 
Then  the  heat  of  dilution  in  large  calories  is 

77? 

D=m{(6-t,}[(Mw+M,)c+w]-(tw-t.)(Mw+w)}. 

The  loss  of  heat  due  to  radiation  must  be  taken  into 
consideration. 

The  specific  heats  of  solutions  may  be  found  in  the  Tables 
of  Landolt  and  Bornstein,  p.  185,  1883. 

Heat  of  Combustion. — The  quantity  of  heat  liberated 
when  one  gram-molecule  of  a  substance  is  completely  burned 
is  known  as  the  heat  of  combustion. 

The  substance  of  which  the  heat  of  combustion  is  to  be 
determined  is  placed  in  a  specially  designed  vessel,  which  i? 
then  filled  with  oxygen  under  definite  pressure.  The  vessel, 
which  is  known  as  the  calorimetric  bomb,  is  introduced 
into  a  calorimeter  and  the  substance  is  then  burned,  the 
heat  liberated  being  absorbed  by  the  water  in  the  calorimeter. 
Let  t  =  initial  temperature  of  calorimeter; 

6  =  final  temperature  of  calorimeter; 
M  =  mass  of  water  in  calorimeter; 
w  =  total  water  equivalent  of  calorimeter; 
m  =  mass  of  substance  burned ; 
p  =  molecular  weight  of  the  substance; 
Cv  =  heat  of  combustion  at  constant  volume ; 
Cp=heat  of  combustion  at  constant  pressure. 
Then  we  have 


114  THERMAL  MEASUREMENTS.  i 

% 
and 

Cp-C.4-0.02g71, 

where  q  denotes  the  number  of  gram-molecules  of  gas  which 
disappear  in  the  reaction,  and  T  denotes  the  absolute  tem- 
perature. 

The  reduction  of  the  heat  at  constant  volume  to  heat  at 
constant  pressure  at  18°  for  solids  and  liquids  of  the  for- 
mula C-flyOz  is  made  by  the  formula 


I-)- 


Cp =CV+  0.291  ( £ 

Apparatus. — The  apparatus  here  described  is  the  At- 
water*  modification  of  the  Berthelot  bomb  calorimeter. 
The  apparatus  consists  of: 

(1)  The  calorimeter  proper,  including  the  bomb,  a  bri- 
tannia-metal  cylinder  to  hold  the  water  in  which  the  bomb 
is  immersed,  a  thermometer  and  a  stirrer. 

(2)  Two  concentric  protecting  cylinders  of   "  indurated 
fibre "  with  cover.     These  inclose  the    calorimeter  system 
and  insulate  it. 

(3)  Accessory  apparatus,  including  appliances  for  filling 
and  closing  the  bomb,  electric  devices  for  igniting  the  sub- 
stance, and  mechanism  for  operating  the  stirrer. 

The  Bomb. — The  bomb  consists  of  three  parts:  A  cylin- 
drical cup  to  contain  the  substance  to  be  burned  and  the 
oxygen  for  combustion,  a  cover  to  close  the  cup,  and  a 
threaded  ring  or  collar  to  hold  the  cover  tightly  on  the  cylin- 
der. With  these  is  a  metal  capsule  to  hold  the  substance. 
The  parts  are  shown  assembled  in  Fig.  48.  The  cup  is  of 
the  best  tool-steel,  as  are  also  the  cover  B,  collar  C,  and  the 
screws  E,  F.  The  approximate  dimensions  of  the  cup  are: 

*  Atwater  and  Snell,  Jour.  Am.  Chem.  Soc.,  25,  659,  1903. 


CALORIMETRY. 


115 


Depth,  13  cm. ;  diameter,  6  cm.  at  top  and  5.5  cm.  at  bottom. 
The  wall  is  a  little  over  0.5  cm.  in  thickness.  The  weight  is 
about  3  kg.,  and  the  capacity  a  little  over  350  c.c. 

The  cover  is  lined  on  the  bottom,  and  is  provided  with  a 
neck,  D.    Into  this  fits,  at  the  top,  a  cylindrical  screw,  E, 


FIG.  48. 

into  which  in  turn  fits  a  valve-screw,  F.  In  the  neck  D, 
where  the  bottom  of  the  cylindrical  screw  E  rests,  is  a  shoul- 
der fitted  with  a  packing  of  lead,  L.  The  pressure  of  the 
valve-screw  on  this  packing  makes  a  tight  closure  upon  the 
part  of  F  which  it  surrounds.  On  the  side  of  D  is  an  open- 
ing, G,  into  which  may  be  screwed  the  coupling  connecting 
the  tube  with  the  receptacle  which  holds  the  oxygen  used 
for  the  combustion. 


116  THERMAL  MEASUREMENTS. 

The  coupling  when  screwed  in  thrusts  against  a  washer 
of  lead  at  the  end  of  G  which  insures  perfect  closure.  A 
narrow  passage  runs  horizontally  to  a  point  just  above  the 
valve-seat  in  the  centre  of  D.  A  similar  passage  runs  from 
the  apex  of  the  valve-seat  perpendicularly  downwards 
through  the  cover. 

These  two  passages  provide  a  channel  for  the  oxygen  to 
pass  into  the  interior  of  the  bomb. 

This  channel  may  be  tightly  closed  by  the  valve-screw, 
the  lower  end  of  which  is  conical  and  thrusts  against  the  inner 
surface  of  D,  the  angle  of  which  at  the  place  of  contact  corre- 
sponds to  that  of  the  tip  of  the  screw.  Between  the  top  of 
the  valve-seat  and  the  bottom  of  the  packing  L  the  valve- 
screw  fits  so  closely  in  the  cover  as  to  prevent  the  lead  of  the 
packing  from  working  downward  and  thus  obstructing  the 
small  gas-passages. 

The  upper  edge  of  the  cup  A  is  bevelled  on  both  sides ;  the 
apex  is  rounded  and  fits  into  a  gasket,  K,  of  lead,  which  is 
held  in  a  groove  in  the  cover  B.  The  platinum  wires  H  and  / 
inside  the  bomb  serve  to  hold  the  capsule  0  containing  the 
substance  to  be  burned  and  to  conduct  an  electric  current 
for  igniting  it.  Of  these  two  wires,  one,  7,  is  screwed  into  the 
cover;  the  other,  H,  passes  through  a  conical  hole  and  is 
insulated  from  the  metal.  Near  the  lower  end  of  H  is  a 
platinum  wire  bent  in  the  form  of  a  ring  to  hold  the  capsule, 
and  coiled  about  the  wire,  to  which  it  is  held  by  a  platinum 
thumb-nut.  When  a  combustion  is  made  the  two  platinum 
wires  are  connected  by  a  very  fine  iron  wire  which  passes 
over  the  capsule  and  is  heated  by  the  electric  current.  The 
part  directly  above  the  substance  to  be  burned  is  wound  into 
a  spiral,  thus  furnishing  a  larger  quantity  of  iron  to  be  ignited 
and,  falling,  to  ignite  the  substance  in  the  capsule. 

The  cup  and  the  cover  are  lined  with  gold-plated  copper. 


CALORIMETRY.  117 

The  lining  of  the  cup  is  made  from  a  single  sheet  of  metal, 
which  is  spun  to  fit  the  steel  cup  accurately.  It  can  be  easily 
removed  from  the  latter  by  placing  the  fingers  of  the  left  hand 
inside  the  lining,  and  the  thumb  against  the  threads  of  the 
cap,  and  drawing  outward  upon  the  lining,  at  the  same  time 
tapping  the  steel  cup  with  a  wooden  mallet. 

The  sample  for  combustion  is  held  in  a  metal  capsule 
which  is  supported  in  the  bomb  as  shown  in  Fig.  44.  The 
capsule  is  made  of  sheet  nickel  0.4  mm.  in  thickness.  It  is 
1.7  cm.  deep,  1.5  cm.  in  diameter  at  the  base  and  2.2  cm.  in 
diameter  at  the  top. 

The  ignition  of  the  sample  is  effected  by  means  of  a 
small  coil  of  iron  wire  heated  to  ignition  by  an  electric  cur- 
rent. 

The  thermometer  used  is  of  the  ordinary  Beckmann  type, 
graduated  to  T-J-Tr  of  a  degree. 

When  ready  for  a  combustion  the  bomb  is  immersed  in 
water  contained  in  a  small  metal  cylinder. 

This  cylinder  is  surrounded  by  concentric  cylinders  of 
'ndurated  fibre,  leaving  air-spaces  to  prevent  undue  passage 
of  heat  between  the  water  and  the  outer  air.  The  assembled 
apparatus  is  shown  in  section  in  Fig.  49.  The  cylinder 
is  of  Britannia  metal,  13  cm.  in  diameter,  23  cm.  high, 
and  holds  with  the  bomb  not  far  from  2  litres  of  water.  A 
stirrer,  SS,  moved  by  a  small  motor  keeps  the  water  in  motion 
and  insures  the  mixture  needed  for  equalizing  its  tempera- 
ture. The  stirrer  consists  of  two  perforated  annular  pieces 
of  sheet  brass  connected  by  two  brass  rods  which  project 
out  of  the  calorimeter  and  are  there  attached  by  thumb- 
screws to  a  nickel-plated  cross-piece.  A  groove  is  cut  in 
one  side  of  the  annular  pieces  to  admit  the  thermometer. 
The  calorimeter  stands  on  cork  supports  which  prevent  it 
from  coming  in  contact  with  the  bottom  indurated-fibre 


118 


THERMAL  MEASUREMENTS 


vessel.    The  diameters  of  the  indurated-fibre  vessels  U  and  T 
are  such  as  to  leave  an  air-space  of  about  1  cm.  between 


FIG,  49. 

the  two  vessels  and  one  of  3  cm.  between  the  inner  vessel 
and  the  calorimeter  cylinder.    The  covers  of  the  vessels  are 


CALORIMETRY.  119 

of  hard  rubber.  They  are  provided  with  holes  for  two 
rods  of  the  stirrer  and  the  thermometer. 

Accessory  Apparatus.  —  The  stirring-apparatus  may  be 
operated  either  by  a  small  hot-air  engine  of  •£•$  horse- 
power, or  a  small  electric  motor  of  the  same  power.  The 
substance  is  ignited  by  means  of  a  current  of  from  3  to  4 
amperes,  which  may  be  obtained  from  the  110-volt  street 
current  by  sending  it  through  four  32-candle-power,  110-volt 
lamps  in  parallel.  The  substance  to  be  burned,  if  in  the 
solid  state,  is  usually  pressed  into  small  pellets  in  a  pellet- 
press.  The  oxygen  used  is  obtained  in  steel  cylinders, 
each  of  which  should  contain  enough  oxygen  for  250  deter- 
minations. Brass  coupling-tubes  serve  to  connect  the  cylin- 
der with  a  manometer  and  the  bomb.  By  means  of  the 
manometer  one  can  tell  when  the  supply  of  gas  is  nearly 
exhausted. 

General  Test  of  the  Apparatus. — "  The  general  condition 
of  the  apparatus  should  be  tested  from  time  to  time  by 
check  combustions.  Benzoic  acid  and  cane-sugar  are  con- 
venient substances  for  this  purpose,  because  they  are  easily 
obtained  pure  and  their  heats  of  combustion  are  accurately 
known."  "The  benzoic  acid  has  the  advantage  over  the 
sugar  that  the  pellets  do  not  clog  the  pellet-mould  and  that  no 
kindler  other  than  the  iron  wire  is  needed  for  the  ignition." 

METHOD  OF  USE  OF  THE  APPARATUS. — Quantity  of  Sub- 
stance to  be  Used. — "  The  quantity  of  material  burned  in  the 
bomb  should  be  such  as  will  yield  from  4000  to  7000  calories." 

"  Of  substances  which  have  been  found  convenient  for 
tests  of  the  accuracy  of  the  determinations,  the  following  are 
suitable  quantities: 

Naphthalene  and  camphor 0 . 5  to  0 . 7  gram 

Benzoic  acid  and  hippuric  acid 0 . 7  to  1 . 0  gram 

Cane-sugar  and  glycocoll 1  to  2 . 0  gram." 


120    .  THERMAL  MEASUREMENTS. 

Preparation  of  the  Material  for  Combustion.  —  Solids. 
"  Solids  in  general  are  powdered  and  pressed  into  cylindrical 
pellets  in  the  pellet-mould  as  described  above.  The  material 
is  weighed  approximately  before,  and  accurately  after, 
moulding." 

"With  some  substances  special  devices  are  required  to 
secure  ignition.  A  crystal  of  naphthalene  serves  as  a  kindler 
for  such  substances  as  sugar  and  glycocoll.  The  naphtha- 
lene may  be  inserted  between  two  turns  of  the  coiled  iron 
wire  with  one  edge  touching  the  substance  in  the  capsule. 
Or,  instead  of  a  coil,  the  wire  may  be  formed  into  a  loop 
resembling  one  of  the  forms  of  wire  office-clips  used  for  hold- 
ing sheets  of  paper  together,  and  the  naphthalene  placed  in 
the  loop,  which  should  touch  the  substance  in  the  capsule." 

"Substances  which  are  still  more  difficult  to  ignite,  e.g., 
creatin  and  creatinin,  may  be  enclosed  in  gelatin  capsules, 
such  as  are  used  with  volatile  liquids  (see  below)." 

Oils. — "Oils  are  absorbed  in  fibrous  asbestos.  The 
metal  capsule  is  half-filled  with  asbestos,  ignited  in  a  Bunsen 
flame,  cooled  in  a  desiccator  and  is  weighed  before  and 
again  after  addition  of  the  oil." 

Volatile  Liquids. — "Volatile  liquids,  e.g.,  alcohol, 
may  be  enclosed  in  gelatin  capsules.  We  have  found  the 
'Beekman  ideal'  capsule  No.  00,  which  weighs  from  0.11  to 
0.19  gram,  very  convenient  for  the  purpose." 

Filling  the  Bomb. — "The  bomb-cover  being  supported 
upon  a  ring-stand,  the  capsule  containing  the  pellet  is  placed 
in  position  in  the  platinum  ring.  The  ends  of  the  coil  of  iron 
wire  are  wound  around  the  vertical  platinum  wires  (one 
turn  only)  and  the  coil  adjusted  so  that  it  touches  the  sub- 
stance to  be  burned,  but  not  the  capsule.  The  naphthalene 
(if  any  is  to  be  used)  is  placed  in  position.  The  cover  is  now 
placed  on  the  bomb  and  a  little  oil  dropped  upon  the  top  to 


CALORIMETRY.  121 

prevent  its  turning  with  the  collar,  which  is  then  screwed  on 
and  tightened  by  means  of  a  clamp  and  spanner.  The 
bomb  is  now  ready  to  be  filled  with  oxygen.  With  its  valve 
slightly  open  it  is  placed  in  position  on  an  iron  shelf  and 
connected  with  the  manometer,  which  is  kept  permanently 
connected  with  the  oxygen  cylinder.  The  valve  of  the 
oxygen  cylinder  is  then  opened  cautiously.  When  the 
manometer  indicates  a  pressure  of  20  atmospheres  the 
oxygen  is  cut  off,  the  bomb-valve  closed,  and  the  bomb 
disconnected  from  the  manometer." 

"  Leakage  of  gas  from  the  bomb  may  occur  either  at  the 
soft-metal  gasket  (K)  or  at  the  conical  tip  of  the  valve- 
screw  (F)  (Fig.  48).  Gas  escaping  at  the  gasket  will  usually 
make  an  audible  sound.  If  the  gasket  is  not  too  much  worn, 
the  leak  may  be  stopped  by  screwing  the  collar  tighter.  A 
leak  at  the  valve  can  be  easily  and  quickly  detected  by  placing 
the  moistened  finger  over  the  opening  (G).  When  the  valve- 
tip  or  the  conical  shoulder  into  which  it  fits  becomes  cor- 
roded so  that  the  valve  cannot  be  closed  by  gentle  pressure, 
it  must  be  reseated  carefully  in  a  lathe  to  secure  a  proper 
fit.  If,  in  filling  the  bomb,  leakage  occurs  at  L  (Fig.  48), 
the  cylindrical  screw  (E)  should  be  tightened  a  little  to  press 
the  packing  (L)  tightly  around  the  valve-screw. " 

Arranging  Apparatus  for  the  Combustion. — "The  calo- 
rimetric  water  should  now  be  put  in  the  Britannia-metal 
cylinder.  Both  the  quantity  and  the  temperature  of  this 
water  are  to  be  regulated.  In  order  to  facilitate  the  calcu- 
lations, it  is  better  to  make  the  quantity  always  the  same 
and  such  that  the  total  hydrothermal  value  of  the  calorimeter 
system  will  be  a  round  number,  such  as  2000,  2100,  or  2200 
grams.  In  order  to  reduce  to  a  minimum  the  correction  for 
the  influence  of  the  surroundings  upon  the  temperature  of 
the  system,  the  water  in  the  cylinder  should  be  made  cooler 


122  THERMAL  MEASUREMENTS. 

than  the  surroundings  of  the  system  (as  measured  by  an 
ordinary  thermometer  placed  in  the  inner  air-space)  by 
about  the  expected  rise  in  temperature,  or  a  little  more. 
For  example,  if  the  quantity  of  substance  to  be  burned  is 
such  as  will  yield  about  6300  calories  and  the  hydrothermal 
value  of  the  system  is  to  be  2100  grams,  the  rise  expected 
will  be  3°  and  the  water  in  the  cylinder  should  be  made 
3°-3.2°  cooler  than  the  air  of  the  inner  air-space.  The  inser- 
tion of  the  bomb,  which  is  at  room  temperature,  will  de- 
crease this  temperature  difference  by  about  one-sixth,  the 
hydrothermal  value  of  the  bomb  being  about  one-sixth  that 
of  the  whole  system,  so  that  after  the  combustion  the  tem- 
perature of  the  system  will  be  a  little  above  that  of  the  sur- 
roundings." 

"It  is,  obviously,  more  convenient  to  adjust  the  temper- 
ature of  the  water  first  and  the  quantity  afterwards.  The 
desired  temperature  can  be  readily  obtained  by  mixing 
cooler  water  with  that  used  in  the  preceding  combustion  (or 
with  a  portion  of  it).  Water  is  then  poured  out  of  the  cylin- 
der until  approximately  the  desired  quantity  remains;  the 
cylinder,  containing  water  and  stirrer,  is  placed  upon  a 
tared  balance,  accurate  to  1  gram,  and  small  quantities  of 
water  are  added  or  removed  until  the  correct  weight  is  ob- 
tained. The  tare  required  is,  of  course,  the  desired  hydro- 
thermal  value  (e.g.,  2100  grams)  minus  the  hydrothermal 
equivalent  of  the  apparatus  and  plus  the  weight  of  the  cylinder 
and  stirrer." 

"The  cylinder,  containing  stirrer  and  water,  is  now  put 
in  place  inside  the  outer  cylinders  and  the  two  conducting 
wires  are  joined,  respectively,  to  the  valve-screw  and  to  the 
insulated  conductor.  The  covers  are  put  on  and  adjusted 
so  that  the  stirrer  will  run  smoothly,  the  thermometer  is 
inserted  and  the  stirrer  set  in  motion.  As  soon  as  the  differ- 
ent parts  of  the  calorimeter  system  have  assumed  a  common 


CALORIMETRY.  123 

temperature,  which  usually  requires  two  or  three  minutes, 
the  mercury  will  begin  to  rise  at  a  uniform  rate,  and 
the  readings  of  the  ' initial'  or  precombustion  period  may 
begin." 

"The  room  temperature  may  have  changed  so  much 
since  the  apparatus  was  last  used  that  the  thermometer 
must  be  reset.  In  that  event  the  water  should  be  stirred 
a  little  after  the  insertion  of  the  bomb  and  its  temperature 
determined  with  an  ordinary  thermometer,  so  that  the 
actual  temperature  to  which  the  zero  of  the  reset  thermome- 
ter corresponds  may  be  known  within  half  a  degree." 

Temperature  Changes  in  the  System. — "  If  the  calorime- 
ter system  were  absolutely  insulated  thermally,  only  two 
temperature  observations  would  be  necessary  for  the  deter- 
mination of  the  heat  of  combustion  of  the  substance.  One 
of  these  could  be  made  at  any  time  after  the  system  had 
come  to  internal  temperature  equilibrium  after  the  insertion 
of  the  bomb,  and  before  the  ignition  of  the  substance,  for 
the  temperature  would  remain  absolutely  constant  during 
this  interval  of  time  whatever  might  be  its  length.  This 
observation  would  give  the  initial  temperature  of  the  sys- 
tem. The  second  observation,  that  of  the  final  temperature, 
could  be  made  at  any  time  after  the  heat  from  the  combustion 
had  distributed  itself  uniformly  throughout  the  system,  for 
then  the  temperature  would  again  remain  constant." 

"  But  it  is  of  course  impossible  to  insulate  the  system 
completely  and,  consequently,  external  influences  are  con- 
tinually affecting  its  temperature.  The  most  obvious  and 
doubtless  the  most  important  of  these  external  influences 
is  the  temperature  of  the  medium  surrounding  the  system. 
This  medium  may  be  regarded  as  made  up  of  (1)  the  air  of 
the  inner  jacket;  (2)  the  walls  of  the  inner  indurated-fibre 
cylinder;  and  (3)  the  air  and  walls  of  the  outer  air-jacket 
and  the  air  of  the  room.  Interchange  of  heat  occurs  be- 


124  THERMAL  MEASUREMENTS. 

tween  the  system  and  (1)  the  air  of  the  inner  air-jacket,  by 
convection  and  radiation;  (2)  the  indurated-fibre  cylinder 
by  radiation;  and  (3)  the  air  of  the  outer  air-jacket  and  of 
the  room  by  conduction  through  and  convection  by  the 
rods  of  the  stirrer.  All  of  these  interchanges  may  be  fairly 
assumed  to  obey  Newton's  Law." 

"The  correction  for  the  ' external  influences'  may,  there- 
fore, be  estimated  on  the  assumption  that  the  rate  of  warm- 
ing or  cooling  of  the  calorimeter  system  m  a  given  minute 
is  proportional  to  the  difference  between  the  average  tem- 
perature of  the  system  for  that  minute  and  the  temperature 
of  the  surrounding  medium.  Further,  the  temperature  of 
the  surrounding  medium  may  be  regarded  as  constant. 
The  correction  for  the  effect  of  external  influences  on  the 
temperature  of  the  system  may,  therefore,  properly  be 
determined  according  to  the  method  of  Regnault,  which  is 
based  upon  the  assumptions  just  mentioned." 

The  Thermometer  Readings. — "  Readings  may  be  begun 
at  any  time  after  the  stirrer  has  been  set  in  motion.  They 
should  be  continued  until  there  has  been  a  uniform  rise  of 
temperature  for  five  minutes,  the  differences  between  suc- 
cessive readings  not  varying  by  more  than  0.002°.  These  five 
minutes  constitute  the  initial  or  precombustion  period. 

"  Precisely  at  the  end  of  the  five  minutes  (i.e.,  at  the  sixth 
reading  of  the  initial  period)  the  electric  circuit  through 
the  fine  iron  wire  in  the  bomb  is  completed  by  closing  a 
switch.  The  resistance-lamps  are  incandescent  during  the 
passage  of  the  current,  and  the  extinction  of  their  light  indi- 
cates that  the  iron  wire  has  been  fused.  This  usually  occurs 
within  two  or  three  seconds  after  the  closing  of  the  circuit. 
The  switch  should  now  be  opened  immediately  to  avoid 
error  from  the  production  of  heat  in  the  calorimeter  by  the 
passing  of  the  current  through  the  water. 

"  Readings  should  be  continued  at  intervals  of  one  minute 


CALORIMETRY.  125 

until  the  rate  of  fall  of  the  mercury  has  become  regular — an 
indication  that  internal  equilibrium  has  been  regained.  This 
marks  the  end  of  the  combustion  period.  In  routine  work, 
however,  it  is  convenient,  for  the  sake  of  uniformity  in  the 
calculations,  to  regard  the  combustion  period  as  ending,  in 
all  cases,  five  minutes  after  the  ignition.  After  the  final 
reading  of  the  combustion  period  the  stirring  is  continued 
for  five  minutes  (final  or  ' postcombustion '  period),  at  the 
end  of  which  time  another  reading  is  taken. 

"  Before  each  reading  the  thermometer  should  be  tapped 
with  the  electric  hammer." 

After  the  Combustion.  — "  The  bomb  is  now  removed 
from  the  calorimeter  and  placed  in  the  clamp.  After  the 
pressure  has  been  relieved  by  opening  the  valve,  the  collar 
is  unscrewed  and  the  cover  removed.  The  interior  of  the 
bomb  and  the  lining  of  the  cover  are  rinsed  with  water  and 
the  rinsings  titrated  to  determine  the  nitric  acid  (see  below). 
The  quantity  of  iron,  if  any,  remaining  unoxidized  must  be 
deducted  from  the  quantity  originally  taken.  It  may  be 
determined  by  weighing  or  (more  conveniently)  by  measur- 
ing its  length  on  a  millimetre  or  other  finely  graduated  scale. " 
Determination  of  the  Nitric  Acid.  — "  The  temperature 
in  the  interior  of  the  bomb  during  the  combustion  is  so 
great  as  to  bring  about  the  combustion  of  some  of  the  atmos- 
pheric nitrogen  left  in  the  bomb  on  filling,  and  also  of  some  of 
the  nitrogen  contained  in  the  substance  burned.  The  prod- 
uct of  this  combustion  is  nitric  acid.  The  heat  produced 
by  the  combustion  of  the  nitrogen  is,  of  course,  to  be  deducted 
from  the  total  heat  measured.  For  the  determination  of 
the  nitric  acid  Stohmann  advises  the  use  of  a  solution  of  sodium 
carbonate  containing  3.706  grams  per  litre.  One  cubic  centi- 
metre of  this  solution  contains  0.003706  gram  sodium  car- 
bonate, which  is  equivalent  to  0.004406  gram  nitric  acid,  the 
heat  of  formation  of  which  J£_or\e  pa}orie.  Thus  each  cubic 

OF  THE  >)L 

IIMIWCTDQITV     \ 


(26  THERMAL  MEASUREMENTS. 

centimetre  of  sodium  carbonate  used  in  the  titration  repre- 
sents one  calorie  set  free  in  the  calorimeter  by  the  combustion 
of  nitrogen.  Methyl  orange  is  ueed  as  indicator." 

DETERMINATION  OF  THE  EQUIVALENT  OF  THE  CALORIM- 
ETER.— "Now  that  the  heats  of  combustion  of  many  com- 
pounds are  accurately  known,  the  most  convenient  and  satis- 
factory method  for  the  determination  of  the  water  equiva- 
lent of  a  bomb  calorimeter  is  to  burn  weighed  quantities  of 
such  compounds  in  the  bomb  immersed  in  a  known  quantity 
of  water.  From  the  observed  rise  of  temperature  and  the 
known  heat  of  combustion  of  the  compound  used  the  total 
water  value  of  the  calorimeter  system  is  calculated.  De- 
ducting from  this  the  quantity  of  water  used,  we  have  the 
water  value  of  the  calorimeter  itself. 

"The  substances  used  in  these  determinations  should  be 
such  as  can  easily  be  obtained  pure  and  preserved  without 
risk  of  change  by  deliquescence,  oxidation,  decomposition,  or 
otherwise.  Their  heats  of  combustion  should  have  been 
determined  in  calorimeters  whose  water  equivalents  have 
been  learned  by  other  methods.  Those  which  have  been 
determined  by  several  investigators,  independently  and 
with  closely  accordant  results,  are  to  be  preferred." 

"Camphor,  hippuric  acid,  and  benzoic  acid  are  ignited 
directly  by  the  heated  iron  wire,  but  with  cane-sugar  and 
glycocoll  a  kindler  (a  naphthalene  crystal)  should  be  used. " 

The  following  are  the  specific  heats  of  combustion  of  the 
five  substances  in  question: 

Glycocoll 3131 

Cane-sugar 3959 

Hippuric  acid 5664 

Benzoic  acid 6322 

Camphor 9290 

Calculation  of  Results. — The  method  of  calculating  the 
heat  of  combustion  of  a  substance  together  with  the  mode 


CALORIMETRY. 


127 


of  tabulating  the  data  is  best  explained  by  means  of  an 
example : 


Capsule  No.  1. 

Wt.  caps.  +  subs.   =4.2501 

Wt.  capsule  =2.8783 


CORRECTION   FOR   ACCESSORY   COMBUSTIONS. 

Wt.  Fe  13.0  -1.1=11.9  mgs.  =19.0  cal. 
Wt.  naphthalene  =    6.4     "      =61.6    " 
HNO,  =   6.6    " 


Wt.  substance,  17=1.3718 

Correction  for  accesories    =87.2    " 

INITIAL  PERIOD. 

READ- 
INGS. 
1       1.018 
2       1.021 

3     1.025 
4     1.027 
5     1.030 
600  1.032 

CORRECTED 
READINGS. 
1.015 

1.029 

INITIAL  PERIOD. 

Fall         =  -  .014 
Rate  7  =-.0028 

Mean*0,  0=   1.022 

CORRECTED  READ- 
ING,         05=3.646 
00=1.029 

THERMOMETER 
TION. 

T°air 
.  °  water 
1st  reading 

T°  of  zero 
Corr.  for  1° 
Rise  (degrees) 

Ther.  corr. 

CORREC- 
=  25.2 

=  23.8 
=    1.0 

=  22.8 
=  +  .001 
2  6 

MAIN  PERIOD. 

'    70!  2.300 
802  3.650 
9033.678 
1004  3.662 
.1105  3.653 

2.3 
3.7 
3.7 
3.7 

2.3 

=  15.7 
=   5.1 

=  10.6 

=  0253 
=  7324 

=  +  .0026 

FINAL    CALCULATION. 

05                        =  3.646 

0                                          1   O9Q 

FINAL  PERIOD. 

05  +  00 

Th.  corr. 
Rad.  corr. 

Corr.  rise 
"       "X2100i 
=  Total  heat      ! 
Accessories 

Corrected  heat 

Log.  corr.  heat 
Log.  W 

HEAT    OF            1 
COMBUSTION   !• 
PER  GRAM         J 

05  +  00 
J 

FINAL 

Fall 
Rate  V 
V 

V'-V 
Mean  t°, 

=  4.675 
=  2.3 

PERIOD. 
=  +  .013 

=  +  .0026 

=  2.617 
=  +  .0026 
=  +  .0079 

2 
Sum 
50 

Diff. 

Log.  diff. 
Log.  V'-V 
Colog  0'-0 

Antilog. 
+  57 

Radia-     -j 
tion  cor-  |- 
rection 
I    16        3.( 
Time  3.30 

=   26275 
52550 

=  5517.8 

=       87.2 

—  5^20 
3397 

=  +    .0219 
=  -    .014 

=  +  .0079 
>40  |  3.633 

—  —  .(JOZo 
=  +  .0054 

0'  =  3.640 
0  =1.022 

=  5340.6 

=     73485 
13729 

59756 
=     3959 

0'  -0=2.618 

128  THERMAL  MEASUREMENTS. 

Heat  of  Formation. — The  amount  of  heat  liberated  or 
absorbed  in  the  formation  of  one  gram-molecule  of  a  sub- 
stance is  known  as  the  heat  of  formation. 

If  the  heat  of  combustion  of  the  substance  is  known,  this 
can  be  calculated  according  to  the  principle  laid  down  by 
Hess.  If  the  heat  of  combustion  of  a  compound  be  sub- 
tracted from  the  sum  of  the  heats  of  combustion  of  its  ele- 
ments, the  remainder  is  the  heat  of  formation.  For  exam- 
ple, the  heat  of  formation  of  methane  is  determined  by 
measuring  the  heat  of  combustion  of  the  compound  in  oxygen 
and  the  heats  of  combustion  of  its  elements  in  oxygen : 

C,H4  =  C,02  +  2(H2,0)-CH4,04. 
21,750  =  96,960+136,720-211,930. 

The  heat  of  formation  of  methane  is  thus  21,750  calories. 


OPTICAL  MEASUREMENTS. 


CHAPTER  VIII. 

THE  SPECTROSCOPE. 

THE  apparatus  used  by  the  physical  chemist  for  the 
approximate  determination  of  wave-lengths  and  for  spec- 
trum analysis  is  the  spectroscope  of  Bunsen  and  Kirchhoff. 
This  apparatus  is  shown  in  Fig.  50.  It  consists  of  a  col- 

p 

^.^^m 
C 


FIG.  50. 

limator  A,  through  which  the  light  enters,  the  prism  P,  where 
the  rays  of  light  are  dispersed,  the  observing-telescope  B, 
and  the  sea  e-tube  C. 

129 


130  OPTICAL  MEASUREMENTS. 

The  collimator  is  so  adjusted  that  the  rays  which  enter 
the  slit  S  are  rendered  parallel  before  striking  the  prism  P. 

The  width  of  the  slit  can  be  adjusted  by  means  of  a  screw. 
The  lower  half  of  the  slit  is  usually  covered  with  a  small  com- 
parison prism  by  means  of  which  it  is  possible  to  compare 
two  spectra  directly  without  reference  to  a  table  of  wave- 
lengths. 

The  observing-telescope  serves  to  form  the  image  of  the 
spectrum.  The  eyepiece  is  furnished  with  cross-wires  which 
enable  the  observer  to  set  the  telescope  upon  a  definite  spec- 
tral line. 

The  image  of  the  scale  in  the  tube  C  is  reflected  from  one 
face  of  the  prism  into  the  observing-telescope :  this  image  is 
visible  just  above  the  image  of  the  spectrum.  The  positions 
of  definite  lines  of  the  spectrum  can  be  determined  by  means 
of  the  relative  positions  of  the  lines  and  scale  divisions. 

Adjustment  of  the  Spectroscope.* — (1)  The  slit  must  ap- 
pear as  a  very  distant  object.  After  adjusting  the  eye-piece 
of  the  telescope  so  that  the  cross-wires  appear  sharp,  the 
telescope  is  removed  and  focussed  on  some  distant  object, 
such  as  a  tree  or  brick  wall.  When  this  has  been  accom- 
plished the  telescope  is  replaced,  directed  to  the  slit,  and  the 
latter  drawn  out  until  it  appears  clear  and  sharp. 

(2)  The  prism  must  be  adjusted  to  the  position  of  mini- 
mum deviation.  The  slit  is  illuminated  by  the  sodium 
flame  and  the  prism  placed  approximately  in  the  correct  posi- 
tion before  the  lens  of  the  collimator.  When  the  direction 
of  the  refracted  ray  has  been  found  with  the  naked  eye, 
the  image  of  the  slit  is  sought  with  the  telescope.  The  prism 
is  then  turned  (following  the  image,  if  necessary,  with  the 
telescope)  until  the  image  stops  and  commences  to  move 
backwards.  The  prism  is  then  fixed  in  this  position. 
*  Kohlrausch,  Physical  Measurements. 


THE  SPECTROSCOPE.  131 

(3)  The  reflected  image  of  the  scale  should  be  clearly 
visible.     It  is  illuminated  by  a  gas-jet  placed  about  20  cm. 
from  it.     When  by  turning  the  tube  the  image  is  found,  the 
length  of  the  tube  is  adjusted  until  the  image  of  the  scale 
appears  sharp.    The  images  of  the  slit  and  scale  should  not 
change  their  relative  positions  on  moving  the  eye  before  the 
eyepiece. 

(4)  The  middle  of  the  sodium  lines  should  be  made  to 
coincide  with  the  100th  division  of  the  scale.    This  adjust- 
ment is  made  by  turning  the  scale-tube  until  coincidence  is 
attained;   the  tube  should  then  be  clamped. 

Reduction  of  Scale-readings  to  Wave-lengths. — It  is 
usual  to  express  the  positions  of  spectral  lines  in  wave- 
lengths rather  than  in  terms  of  an  arbitrary  scale. 

In  order  to  determine  the  wave-lengths  which  corre- 
spond to  the  various  points  of  the  scale,  the  positions  of 
certain  characteristic  lines  of  known  wave-length  are  care- 
fuUy  determined. 

A  series  of  salts  giving  lines  throughout  the  whole  visible 
spectrum  are  vaporized  in  a  Bunsen  burner  before  the  slit. 
The  following  lines  are  chosen  as  being  particularly  well 
adapted  to  the  purpose: 


Elements. 
Potassium  red  1 

Wave-lengths  in 
Millionths  of  a 
Millimetre. 

ne  Ka         768 
'    K<?        404.6 
1    Lia         670.8 
'    Na        589.0-589.6 
'    Tl         534.9 
'    Sw        460.8 

"          blue 

Lithium  red.     .  .    .        .    .... 

Sodium  yellow 

Thallium  green  

Strontium  blue..  . 

The  positions  observed  are  plotted  as  abscissae  on  coor- 
dinate-paper, while  the  corresponding  wave-lengths  are  laid 
off  as  ordinates.  The  curve  drawn  through  the  points  thus 
obtained  enables  the  observer  to  express  any  scale  reading  in 


132  OPTICAL  MEASUREMENTS. 

terms  of  wave-lengths.  It  is  obvious  that  this  curve  must 
be  prepared  with  great  care.  The  substances  employed 
must  be  of  a  high  degree  of  purity.  The  chlorides  are  usu- 
ally employed,  though  sodium  chloride  is  inconvenient  on 
account  of  decrepitation,  and  hence  the  carbonate  is  used. 
The  substances  are  introduced  into  the  colorless  Bunsen 
flame  on  a  clean  platinum  wire,  the  glowing  portion  being 
placed  so  far  down  that  no  continuous  spectrum  appears. 
The  slit  should  be  narrow  at  first  in  order  to  separate  any 
lines  which  may  be  close  together,  and  then  the  observation 
should  be  repeated  with  a  somewhat  wider  slit  to  insure  the 
detection  of  fainter  lines. 

Should  the  intensity  of  the  light  diminish,  it  may  fre- 
quently be  restored  by  moistening  the  bead  with  hydro- 
chloric acid,  thus  converting  the  oxide  of  the  metal  into  the 
chloride.  The  platinum  wire  should  be  cleaned  by  moisten- 
ing with  hydrochloric  acid,  and  then  igniting  before  the 
blast-lamp  until  no  color  is  imparted  to  the  flame. 

The  flame  will  always  be  more  or  less  colored  with  sodium, 
and  the  lower  portion  of  the  flame  will  give  faint  green  and 
blue  lines.  Care  must  be  taken  to  cut  off  extraneous  light. 
The  prism  should  be  covered  either  with  the  cover  furnished 
with  the  instrument  or  with  a  black  cloth.  A  black-paper 
screen  should  also  be  placed  around  the  eyepiece  of  the 
telescope  to  shield  the  eye  from  the  illuminating  flame.  All 
of  the  optical  measurements  described  should  be  made  in  a 
dark  room  the  walls  of  which  are  painted  with  lampblack. 

The  scale  should  not  be  illuminated  more  strongly  than 
is  necessary  to  secure  sharp  readings,  and  in  cases  where  the 
lines  are  very  weak  the  light  illuminating  the  scale  should  be 
extinguished. 

Absorption  Spectra. — Liquids  and  solutions  give  almost 
without  exception  broad  absorption  bands,  the  width  of  the 


THE  SPECTROSCOPE.  133 

bands  depending  upon  the  concentration  and  the  thickness  of 
the  layer  of  liquid. 

The  solution  to  be  examined  is  placed  in  a  glass  cell  with 
parallel  sides  between  the  flame  and  the  slit.  The  best  illu- 
minant  is  the  Welsbach  light.  To  eliminate  the  influence 
of  temperature  on  the  absorption  the  solution  should  be 
kept  within  a  few  degrees  of  room  temperature. 

It  is  of  importance  to  know  not  only  the  positions  but 
also  the  intensities  of  the  lines  and  bands  of  an  absorption 
spectrum.  The  results  are  best  recorded  by  photography,* 
but  since  this  requires  an  outfit  not  often  found  in  physico- 
chemical  laboratories,  the  spectrum  is  sketched.  The  lines 
and  bands  are  represented  by  black  lines  of  equal  length  and 
varying  width,  or  by  a  curve  where  abscissae  denote  wave- 
lengths or  scale  divisions,  and  ordinates  correspond  to  esti- 
mated intensities.  The  positions  of  maximum  darkness  in 
an  absorption  spectrum  must  be  obtained  with  the  greatest 
care. 

Spectrophotometry. — By  the  term  spectrophotometry  is 
understood  the  measurement  of  the  amount  of  absorption 
for  a  definite  portion  of  the  spectrum  when  the  light  is 
caused  to  pass  through  an  absorbing  medium.  Of  the  many 
methods  which  have  been  devised  for  the  measurement  of 
absorption,  that  of  Vierordt  is  best  adapted  to  the  needs  of 
the  physical-chemist.  This  method  depends  upon  the  use 
of  a  spectroscope  the  collimator  of  which  is  provided  with  a 
double  slit.  The  intensity  of  the  light  is  proportional  to 
the  width  of  the  slit.  If  the  slits  be  illuminated  by  two 
lights  of  different  intensities,  two  spectra  in  contact,  one 
above  the  other,  will  be  observed:  by  adjusting  one  slit  it 
will  be  possible  to  bring  the  two  spectra  to  equal  intensities, 

*  Ostwald,  Zeit.  phys.  Chem.,  9,  p.  582,  1892. 


134  OPTICAL  MEASUtiEMENTS. 

when  the  ratio  of  the  widths  of  the  slits  will  be  proportional 
to  the  intensities  of  the  two  lights.  The  absorption  coeffi- 
cient a  is  defined  by  the  equation 


where  i  is  the  intensity  of  the  transmitted  light,  iQ  the  intensity 
of  the  incident  light,  d  the  thickness  of  the  absorbing  layer, 
and  e  the  base  of  the  natural  system  of  logarithms. 
From  this  equation  we  see  that 


or  in  Briggsian  logarithms,  making  —  =  A,  we  have 


If,  as  is  customary,  d  be  made  1  cm.,  we  have 

A—  logf 

t-0 

The  absorption  coefficient  A  may  be  defined  as  the  recip- 

i 
rocal  of  the  thickness  d}  which  makes   —  log  —  =  1.     That 

/lo 

is,  the  equivalent  of  writing  i  =  TVv    The  thickness  then  is  that 
value  of  d  which  weakens  the  incident  light  one-tenth. 

If  the  concentration  of  a  solution  is  denoted  by  c,  then 
when  cd  =  constant  we  have  equal  absorption.  If  for  a 
definite  concentration  the  absorption  coefficient  A0  has 
been  found,  and  if  for  concentration  c  the  absorption  coeffi- 
cient A  has  been  determined,  then 


and 


THE  SPECTROSCOPE. 


135 


Thus  it  becomes  possible  to  measure  the  concentration  of  a 
solution  from  the  determination  of  the  ratio  — .     The  specific 

^0 

absorption  coefficient  is  denned  as  the  negative  logarithm  of 

v 
the  ratio  —  when  1  gram  of  substance  is  dissolved  in  1000  c.c. 

'o 

of  solvent  and  observed  wit'h  a  Schulz  glass  (see  below)  1  cm. 
thick. 

k 


FIG.  51. 


Apparatus. — The  apparatus  used  is  the  universal  spec- 
trometer of  H.  Kriiss  (Fig.  51).  This  instrument  is  a  modi- 
fied form  of  the  Bunsen  apparatus.  The  essential  points 
of  difference  are:  (1)  the  various  parts  of  the  apparatus 
have  been  permanently  adjusted  by  the  maker;  (2)  the 
measuring  device  is  especially  accurate;  (3)  the  instrument 
is  furnished  with  an  arrangement  on  the  slit  tube  for  quan- 
titative measurements  by  the  Vierordt  method;  and  (4) 
there  is  also  placed  in  front  of  the  slits  a  Hiifner-Albrecht 
rhomb  (Fig.  52)  in  such  a  position  that  its  edge  just  falls  at 
the  edge  of  the  slits.  In  addition  to  the  spectrophotometer 
there  is  needed  a  Schulz  glass  and  a  Welsbach  lamp.  The 


136 


OPTICAL  MEASUREMENTS 


liquid  to  be  examined  is  placed  in  a  glass  cell  with  parallel 

D 


FIG.  52. 


sides  (Fig.  53)  and  11  mm.  in  thickness.     Within  this  vessel 


a 


FIG.  53. 

is  placed  the  Schulz  glass  (a),  a  rectangular  prism  10  mm. 
in  thickness. 


THE  SPECTROSCOPE. 


137 


The  light  must  thus  pass  through  a  layer  of  liquid  either 
1  mm.  or  11  mm.  in  thickness. 

The  path  of  the  rays  through  the  absorption  cell  and  the 
Hufner-Albrecht  rhomb  is  shown  in  Fig.  54.  It  is  well  to 


FIG.  54. 

interpose  a  ground-glass  plate  between  the  ourner  and  the 
cell,  as  shown  in  the  sketch,  so  as  to  obtain  a  large,  uniformly 
illuminated  field. 

Mat  hod  of  Operation. — The  two  halves  of  the  slit  must  be 
equally  ill uminated  by  the  Welsbach  lamp.  To  establish  this 
condition  one  slit  is  opened  30  divisions  and  the  other  adjusted 
so  that  the  intensities  in  the  green  portion  of  the  spectrum 
are  the  same.  This  adjustment  must  be  repeated  several 
times.  If  the  lamp  is  properly  adjusted,  the  second  slit 
should  be  opened  30  divisions  when  the  two  spectra  are  of 
equa1  intensities.  It  is  essential  that  the  graduated  screw- 
head  should  read  0  when  the  slit  is  closed.  The  vessel  con- 
taining the  liquid  should  be  placed  directly  in  front  of  the 
slit  so  that  the  upper  surface  of  the  Schulz  glass  is  horizontal 
and  in  the  same  plane  with  the  line  bisecting  the  two  halves 
of  the  slit.  This  adjustment  is  made  by  regulating  the  screws 
under  the  stand.  The  Hufner-Albrecht  rhomb  must  be 
adjusted  by  means  of  the  proper  screws  so  that  its  horizontal 
edge  next  to  the  slits  is  -of  the  same  height  and  in  contact 
with  the  line  bisecting  the  distance  between  the  slits,  and  so 


13S  OPTICAL  MEASUREMENTS. 

that  its  horizontal  section  lies  in  the  optic  axis  of  the  col- 
limator. 

The  scale  attached  to  the  telescope  is  used  to  ascertain 
the  wave-lengths  of  the  portion  oi  the  spectrum  examined. 
That  portion  of  the  absorption  spectrum  should  be  used 
where  there  is  no  sudden  change  in  intensity.  The  solution 
should  not  vary  more  than  5°  from  room  temperature. 
Account  must  be  taken  of  the  influence  of  the  solvent  on 
the  value  of  i.  The  following  table  taken  from  Kriiss  gives 
the  adjustments  of  one  micrometer-head  for  various  solvents, 
the  other  micrometer  being  at  100: 

Alcohol,  90% 95.0 

Alcohol  (absolute) 110.0 

Ether  (aqueous) 98 . 0 

Ether  (anhydrous) 91 . 5 

Chloroform  (anhydrous) 112 . 0 

Benzene  (anhydrous) 102 . 5 

Glacial  acetic  acid  (anhydrous) 88.0 

For  accurate  work  it  is  well  not  to  rely  upon  this  table, 
but  to  determine  the  value  for  the  solvent  in  use.  The  con- 
centration of  the  solution  should  be  so  chosen  that  adjust- 
ment to  equal  intensity  requires  the  narrowing  of  the  width 
of  the  slit  from  division  100  to  division  20. 

For  further  details  concerning  spectrophotometry  tne 
student  is  referred  to  Kolorimetrie  und  quantitative  Spec- 
tralanalyse  von  G.  und  H.  Kriiss,  Hamburg  and  Leipzig, 
1892. 

EEFRACTIVE   INDICES. 

The  Pulfrich  Refractometer. — Apparatus. — This  instru- 
ment is  shown  in  Fig.  55.  It  consists  of  a  right-angled 
prism,  the  horizontal  and  vertical  faces  of  which  form  the 
right  angle.  This  prism  is  made  of  highly  refracting  glass, 
and  is  mounted  upon  the  top  of  a  hollow  triangular  support, 


THE  REFRACTOMETER.  139 

which  in  turn  rests  upon  the  base  of  the  instrument.  Upon 
the  upper  surface  of  the  prism,  which  is  slightly  curved,  is 
cemented  a  small  glass  cylinder  provided  with  a  thermometer. 


FIG.  55. 

Into  this  cylinder  the  liquid  to  be  examined  is  placed.  By 
means  of  a  lens  the  rays  of  light  are  brought  to  a  focus  at  the 
base  of  the  small  cylinder  filled  with  liquid.  The  rays  will 
pass  from  the  liquid  into  the  prism,  and  will  emerge  from 


140 


OPTICAL  MEASUREMENTS. 


the  vertical  face  provided  the  angle  formed  with  the  normal 
to  the  surface  is  smaller  than  the  angle  of  total  reflection. 
By  means  of  a  telescope  placed  opposite  the  vertical  surface 
of  the  prism  the  position  of  the  emergent  ray  may  be  found. 
The  telescope  is  provided  with  a  graduated  circle  which 
rotates  with  it,  and  the  eyepiece  is  furnished  with  cross- 
wires.  There  is  also  a  vernier  and  reading-microscope  by 


FIG.  56. 

means  of  which  the  angle  of  rotation  of  the  telescope  may 
be  read  to  minutes  of  arc. 

The  position  of  the  telescope  is  determined  for  which  the 
cross-wires  intersect  upon  the  line  dividing  the  field  of  view 
into  light  and  dark. 

By  substituting  in  a  formula  the  angle  through  which 
the  telescope  has  been  rotated  from  the  zero  of  the  scale  to 
the  required  position,  the  index  of  refraction  of  the  liquid 
can  be  calculated. 

Principle. — In  Fig.  56  is  shown  the  path  of  the  rays 
through  the  liquid  and  the  prism. 

If  N  denotes  the  index  of  refraction  of  the  prism,  n  the 
index  of  refraction  of  the  liquid,  e  the  angle  of  refraction,  and 


THE  REFRACTOMETER.  141 


i  the  angle  of  emergence,  then  we  have 

N_    1 
n     sin  e' 
but 

sin  i 


N~ 


sin  (90° -e) 
sjn  i 
cose 
sin  i 


hence 
and 


The  value  of  n  must  be  less  than  N. 

It  is  obvious  that  the  values  of  both  n  and  N  are  de- 
pendent upon  the  wave-length  of  the  light  used.  Sodium 
light  is  usually  employed.  The  values  of  N  for  sodium, 
lithium,  and  thallium  flames  are: 

N 
Na-1.61511 

Li  =  1.60949 
H  =  1.62043 

Before  using  the  refractometer  it  should  be  tested  with 
pure  water  or  some  other  pure  liquid  of  which  the  refractive 
index  is  accurately  known.  For  water  the  value  of  n  at 
15°  is  1.3336,  and  at  20°  1.3332.  Where  many  measurements 
are  to  be  made  with  the  refractometer  a  table  giving  the 
different  values  of  n  for  corresponding  values  of  i  for  sodium 
light  is  a  great  convenience.  The  results  are  generally 


142  OPTICAL  MEASUREMENTS. 

given  for  angles  differing  by  10',  the  intermediate  values 
being  obtained  by  interpolation. 

Method  of  Operation.  —The  source  of  light  is  placed 
about  fifty  centimeters  from  the  apparatus,  and  by  means  of 
a  sheet  of  white  paper  held  in  front  of  the  cylinder  the 
position  of  the  light  is  adjusted  until  a  sharp,  inverted 
image  of  the  flame  is  obtained.  This  image  should  be  a 
little  above  the  upper  face  of  the  prism,  toward  the  middle 
of  the  cylinder. 

The  liquid  to  be  examined  is  then  introduced  into  the 
cylinder  by  means  of  a  pipette.  The  telescope  is  then 
turned  from  the  normal  position  until  the  .ight  and  dark 
field  is  observed.  The  telescope  is  then  clamped,  and  by 
means  of  the  tangent-screw  the  intersecting  cross-wires  are 
brought  upon  the  line  of  division  between  the  light  and 
dark  fields.  The  angle,  i,  through  which  the  telescope  has 
been  turned  is  then  read  off  to  minutes  of  arc.  Care  must  be 
taken  to  keep  the  temperature  constant  throughout  a  series 
of  determinations,  since  the  refractive  index  changes  with 
the  temperature.  Successive  readings  should  not  differ 
more  than  one  minute:  this  will  insure  the  accuracy  of  the 
determined  refractive  index  to  within  one  unit  in  the  fourth 
decimal  place. 

Care  must  be  taken  in  using  the  instrument  that  the 
glass  cylinder  does  not  become  detached.  Should  this  hap- 
pen, the  cylinder  may  be  replaced  by  a  cement  of  balsam  or 
gum  arabic. 

In  re-cementing  the  cylinder  great  care  must  be  taken 
that,  at  the  place  where  the  light  enters,  the  edge  of  the 
upper  plane  surface  should  be  free  from  cement,  since  sharp 
definition  can  only  be  secured  under  this  condition. 


THE  REFRACTOMETER.  143 

Refraction  Constants. — Of  several  formulas  which  have 
been  proposed  to  express  the  relation  between  chemical 
composition  and  refractive  indices  only  two  need  be  men- 
tioned. These  formulas  are: 

Gladstone  and  Dale  formula, 

fli=^r> a) 

Lorenz-Lorentz  formula, 


where  n  is  the  index  of  refraction  and  d  is  the  density  deter- 
mined at  the  same  temperature  as  n. 

Formula  (2)  is  most  used,  since  it  finds  support  both 
theoretically  and  experimentally. 

If  in  the  above  formulas  either  the  atomic  or  molecular 

volume  is  introduced  in  place  of  the  factor  -^,  the  resulting 

constants  are  known  as  the  atomic  or  molecular  refractions 
respectively.  For  mixtures  the  following  equations  are 
found  to  hold  approximately  : 


.  .  .  =(N-1)V, 
and 


144  OPTICAL  MEASUREMENTS. 

where  v1}  v2 .  .  .  and  nlf  n.2 .  .  .  are  the  volumes  and  refractive 
indices  of  the  components,  and  N  and  V  the  corresponding 
values  for  the  mixture. 

Refractive  indices  may  be  used  to  determine  the  con- 
centration of  a  solution.  For  this  application  of  the  refrac- 
tivity  tee  Schiitt,  Zeit.  phys.  Chem.,  5,  349,  and  9,  349. 

The  determination  of  the  refractive  index  may  also 
serve  to  throw  light  on  the  constitution  of  a  chemical  com- 
pound. The  discussion  of  this  subject  is  out  of  place  here, 
but  the  student  is  referred  to  the  work  of  Briihl  and  others  in 
this  field  * 

The  Polarimeter. — The  polarimeter  is  an  instrument  for 
measuring  the  rotation  of  the  plane  of  polarization.  It  is 
well  known  that  many  solids,  liquids,  and  gases  have  the 
power  to  rotate  the  plane  of  polarization.  If  monochro- 
matic light  be  transmitted  through  a  Nicol  prism,  its  vibra- 
tions are  reduced  to  a  single  plane,  or  it  is  said  to  be  polarized 
If  the  polarized  beam  be  examined  by  means  of  a  second 
similar  Nicol  prism,  there  will  be  found  two  positions  180° 
apart  at  which  the  ray  will  be  transmitted  unobstructed, 
while  in  positions  midway  between  these  two,  viz.,  at  90° 
and  270°,  the  polarized  ray  will  be  completely  cut  off.  These 
two  prisms  are  known  as  the  polarizer  and  the  analyzer. 

If,  when  the  polarizer  and  analyzer  are  so  adjusted  with 
reference  to  each  other  that  no  light  can  pass,  a  tube  con- 
taining some  optically  active  liquid  is  interposed,  the  system 
will  then  transmit  the  incident  light.  By  turning  either  the 
analyzer  or  the  polarizer  a  position  will  be  found  in  which  the 
field  again  becomes  dark.  The  object  of  all  polarimeters  is 


*  Briihl,  Ber.  d.  d.  chem.  Ges.,  12,  2135;  19,  3103.  Briihl,  Liebig's 
Ann.,  200,  139.  Briihl,  Zeit.  phys.  Chem.,  1,  311;  7,  1.  Wallach, 
Liebig's  Ann.,  245,  191.  Kanonnikoff,  Jour,  prakt.  Chem.,  32,  497. 


THE  POLARIMETER.  145 

to  measure  the  angular  rotation  necessary  to  restore  maxi- 
mum darkness. 

The  simplest  conceivable  polarimeter  would  consist  of  a 
polarizer,  polarization-tube,  and  analyzer  fitted  with  a  grad- 
uated circle.  Such  a  polarimeter  was  first  made  by  Biot 
and  later  improved  by  Mitscherlich,  but  since  the  mean 
error  of  the  readings  is  nearly  ±0°.l,  it  finds  little  use  in  the 
physico-chemical  laboratory.  Much  ingenuity  has  been  dis- 
played in  improving  the  polarimeter  and  increasing  its  sen- 
sitiveness, and  as  a  result  many  different  forms  of  apparatus 
are  to  be  found.  The  introduction  of  the  so-called  half- 
shadow  principle  has  increased  the  sensitiveness  of  the  polar- 
imeter to  a  marked  degree.  The  two  forms  of  apparatus 
best  suited  to  the  needs  of  the  physical  chemists  are  the 
polarimeters  of  Laurent  and  Lippich,  both  of  which  are 
half-shadow  instruments. 

The  Laurent  Polarimeter. — The  arrangement  of  parts  hi 
this  apparatus  is  shown  in  Fig.  57.  Sodium  light  enters  the 


P  P 

FIG.  57. 

polarimeter  after  having  traversed  a  plate  of  potassium 
dichromate  crystal,  which  acts  as  a  ray-filter,  thus  insuring 
monochromatic  light.  The  rays  then  enter  the  polarizer  d, 
after  leaving  the  lens  e,  which  renders  them  parallel.  Upon 
emergence  from  the  polarizer  they  enter  a  diaphragm,  /,  one- 
half  of  which  is  covered  with  a  quartz  plate  which  is  cut  par- 
allel to  the  axis,  and  is  of  such  thickness  that  the  rays  of 
sodium  light  are  changed  in  phase  by  one-half  a  wave-length. 
From  the  diaphragm  the  rays  pass  through  the  polarization- 
tube  p,  then  through  the  analyzer  g,  and  finally  through  the 


146 


OPTICAL  MEASUREMENTS. 


eyepiece.  If  the  polarizer  is  so  adjusted  that  the  plane  of 
vibration  of  the  light  is  parallel  to  the  axis  of  the  quartz 
plate,  then,  whatever  the  position  of  the  analyzer,  the  field  of 
view  will  consist  of  two  equally  bright  halves.  If,  however, 
the  polarizer  forms  an  angle  a  with  the  axis  of  the  quartz 
plate,  the  plane  of  polarization  of  the  rays  which  pass  through 
the  quartz  will  be  displaced  in  the  opposite  direction.  Under 
these  circumstances  the  field  of  view  appears  divided  into 
two  halves,  as  shown  in  Fig.  58,  which  for  all  positions  of 
the  Nicol  except  two,  180°  apart,  are  unequally  illuminated. 


FIG.  58. 


The  zero  of  the  instrument  is  this  position  of  uniform 
illumination  of  field.  To  the  eyepiece  and  analyzer  is 
attached  an  arm  carrying  a  vernier  which  moves  over  a 
fixed  graduated  circle. 

The  vernier  can  be  read  by  means  of  a  small  reading- 
microscope.  The  axis  of  the  quartz  plate  and  the  plane  of 
the  polarizer  are  adjusted  to  the  desired  angle  by  means  of  an 
arm  attached  to  the  polarizer. 

The  smaller  the  angle  between  the  axis  of  the  quartz 
plate  and  the  plane  of  the  polarizer  the  more  sensitive  the 
instrument  becomes.  The  polarizer  should  be  adjusted  to 
that  position  for  which  there  is  the  maximum  change  in 
shade  in  the  field  for  a  very  small  rotation  of  the  analyzer. 

The  zero-point  should  be  determined  with  the  tube  filled 
with  pure  water  in  order  that  the  intensity  of  the  field  may 


THE  POLAR1METER. 


147 


be  comparable  with  that  when  the  optically  active  substance 
is  introduced. 

The  intensity  of  the  field  may  be  increased  by  a  slight 
rotation  of  the  analyzer,  but  it  must  be  remembered  that 
increase  in  illumination  is  gained  at  the  expense  of  sensitive- 
ness. 

The  mean  of  the  measurements  180°  apart  should  be 
taken  as  the  true  value  for  the  rotation. 


FIG.  59. 

The  mean  error  for  the  settings  with  the  Laurent  ap- 
paratus may  be  taken  as  ±2  minutes  of  arc.  A  very  serious 
objection  to  the  apparatus  of  Laurent  is  that  it  can  be  used 
with  light  of  only  one  wave-length.  This  difficulty  is  over- 
come in  the  instrument  of  Lippich. 

The  Lippich  Polarimeter. — This  instrument  is  shown  in 
Fig.  59,  and  the  arrangement  of  the  optical  system  is  shown 
in  Fig.  60. 


148  OPTICAL  MEASUREMENTS. 

The  construction  is  very  simple,  and  at  the  same  time 
it  affords  the  best  polarizing  apparatus  known. 

Just  beyond  the  polarizer  N^  there  is  placed  a  small 
Nicol  prism,  N2,  which  is  so  adjusted  that  one  edge  lies  in  the 
axis  of  the  apparatus  and  bisects  the  circular  polarizer  dia- 
phragm D.  The  small  prism  N2,  which  is  called  the  "  half- 
prism/'  is  fixed,  while  the  polarizer  Nt  is  movable  about  the 
axis  of  the  tube,  thus  making  it  possible  to  change  the  half- 
shadow.  The  principal  sections  of  the  prisms  Nt  and  N2. 
may  form  with  each  other  a  small  angle  a,  so  that  the  light 
coming  from  the  polarizer  and  passing  through  the  free  half 

A' 

r 


UGHT\  —- - 


of  the  field  of  view  is  polarized  vertically  to  the  principal 
section  of  Nlt  whereas  the  other  portion  of  the  light  is  broken 
up  into  two  components  oh  entering  N2,  of  which  only  the 
rays  vertical  to  the  principal  section  of  the  half-prism  emerge. 
Hence  the  light  which  comes  through  the  covered  half  of 
the  field  of  view  is  polarized  vertically  to  the  principal  sec- 
tion of  the  prism  N2,  and  the  whole  field  is  composed  of  two 
halves  whose  planes  of  polarization  form  with  each  other  the 
small  angle  a.  The  light  of  each  half  remains  linear  for  all 
wave-lengths,  and  polarized  in  the  same  direction.  There 
is  a  slight  difference  in  the  intensities  of  the  two  halves  of 
the  field  of  view,  owing  to  the  absorption  of  light  in  trans- 
mission through  the  half -prism.  In  the  inital  or  zero  position, 
therefore,  the  principal  section  of  the  analyzer  N9  cannot 
bisect  the  angle  of  half-shadow. 

In  using  the  Lippich  polarimeter  the  angle  a  should  be 
made  as  small  as  possible.     With  a  light  of  medium  bright- 


THE  POLARIMETER. 

ness  and  a  half-shadow  angle  of  1°  the  mean  error  of  reading 
is  about  ±15  seconds  of  arc. 

Lamp  for  Homogeneous  Light. — The  most  convenient 
lamp  consists  of  an  elongated  Bunsen  burner  mounted  upon 
a  heavy  foot  and  furnished  with  a  chimney  of  sheet  iron.  In 
one  side  of  the  chimney  is  an  opening  through  which  the 
flame  can  be  observed.  Upon  the  top  of  a  short  vertical 
support  which  can  be  rotated  there  is  fastened  a  horizontal 
arm  which  carries  upon  its  end  a  small  annular  trough  of 
platinum.  This  trough  may  be  filled  with  sodium  car- 
bonate, and  by  turning  the  support  it  can  be  introduced 
into  the  flame.  Such  a  lamp  will  furnish  an  intense  yellow 
light  for  some  time  without  renewal  of  the  .sodium  car- 
bonate. 

Observing-tubes. — The  ordinary  form  of  observing-tube 
consists  of  a  thick-walled  glass  tube  the  ends  of  which  are 
ground  to  planes  accurately  perpendicular  to  the  axis  of  the 
tube.  To  the  ends  of  the  tube  are  cemented  brass  tubes 
upon  which  deep  threads  are  cut.  Upon  these  brass  tubes 
are  screwed  caps  of  brass  which  press  plane  glass  plates 
firmly  against  the  ends  of  the  observing-tube.  In  order  to 
insure  the  tubes  against  leaking,  and  also  in  order  to  avoid 
the  application  of  too  great  pressure,  the  caps  are  provided 
with  rubber  rings. 

Since  changes  in  temperature  cause  marked  changes  in 
the  optical  activity  of  almost  all  substances,  it  is  almost 
indispensable  to  have  some  device  by  which  the  temperature 
of  the  liquid  within  the  tube  may  be  kept  constant.  By 
surrounding  the  tube  with  a  jacket  similar  to  the  Liebig's 
condenser  it  is  possible  to  circulate  water  of  a  constant 
known  temperature  and  thus  secure  constant  temperature 
within  the  tube.  Since  the  exclusion  of  the  last  air-bubble 
in  filling  an  observing-tube  is  frequently  a  source  of  much 


150 


OPTICAL  MEASUREMENTS. 


vexation,  the  form  of  tube  shown  in  Fig,  61  is  to  be  recom- 
mended. 

Before  using  a  tube  it  must  be  thoroughly  cleaned.  This 
is  accomplished  by  removing  both  caps  and  running  pure 
water  through  the  tube,  after  which  it  is  dried  by  pushing 
through  it  rolls  of  soft  linen  cloth  with  a  wooden  stick.  The 
glass  plates  are  then  carefully  washed  and  dried,  and  one  is 
placed  over  one  end  of  the  tube  and  fastened  down  by  means 


I 


FIG.  61. 

of  the  screw-cap.  Care  must  be  taken  in  fastening  the  plates, 
since  if  too  great  pressure  is  applied  they  become  doubly 
refracting  and  thus  introduce  errors  in  the  subsequent 
measurements.  The  tube  is  then  filled  with  the  liquid  under 
investigation  until  a  flat  meniscus  appears  above  the  upper 
end  of  the  tube.  The  second  plate  is  then  slipped  over  the 
end  of  the  tube  and  fastened  in  place,  care  being  taken  to 
avoid  the  entrance  of  an  air-bubble.  The  tube  is  then 
placed  in  position,  and  when  it  has  acquired  the  desired 
temperature  the  readings  are  taken.  In  all  measurements 
with  the  polarimeter  an  initial  reading  must  be  taken  with 
the  tube  filled  with  pure  distilled  water.  The  polarimeter  is 


THE  POLAWMETER.  151 

ordinarily  furnished  with  several  tubes  of  varying  length, 
the  lengths  being  indicated  on  the  tubes. 

Specific  Rotation. — The  specific  rotation  of  an  optically 
active  liquid  is  the  rotation  produced  by  a  column  of  liquid 
10  cm.  in  length.  If  the  liquid  is  a  solution,  it  is  the  rotation 
produced  by  a  column  of  the  solution  10  cm.  in  length,  the 
solution  containing  1  gr.  of  substance  in  1  c.c.  of  volume. 

Denoting  the  density  of  the  solution  by  d,  the  length  of 
the  column  in  decimetres  by  I,  and  the  rotation  produced  by 
a,  then  the  specific  rotation  A  for  light  of  a  definite  wave- 
length is 

*-* 

Molecular  Rotation. — The  molecular  rotation  is  the  rota- 
tion produced  by  one  gram-molecule  of  the  substance,  or 


ma      mA 
lOOdZ =  100' 


The  arbitrary  factor  100  is  introduced  to  avoid  large  num- 
bers. 

For  a  solution  containing  C  grams  of  substance  in  100  c.c. 
of  solvent  the  specific  rotatory  power  for  the  concentration 
given  is  calculated  from  the  formula 


or 


152  OPTICAL  MEASUREMENTS. 

On  the  other  hand,  if  g  grams  of  substance  are  contained  in 
100  gr.  of  solution  of  density  d,  then  the  specific  rotatory 
power  is 

IQOo: 

or 

'        M-  — 

IrJ.  —  7      7  • 

Igd 

Rotation  Dispersion. — The  degree  of  rotation  produced 
by  an  active  liquid  is  dependent  upon  the  wave-length  of 
the  light  employed.  The  rotation  is  greatest  for  the  violet 
and  least  for  the  red,  the  amount  of  rotation  therefore  increas- 
ing with  decrease  in  wave-length.  Biot  first  proposed  a 
formula  connecting  the  amount  of  rotation  with  wave-length, 
but  this  was  later  found  to  be  only  an  approximation. 

The  two  formulas  which  are  accepted  to-day  as  nearly 
correct  are  those  of  Boltzmann  and  Lommel,  which  are 
respectively 

A     B 


(where  A  and  B  are  constants)  and 


'('-¥)' 


(where  a  and  A0  are  constants). 

The  values  of  these  constants  are  determined  by  measur- 
ing the  rotations  alt  a2,  «3,  etc.,  produced  by  light-waves  of 
known  lengths  A,,  A2,  A3,  etc.,  and  then  solving  the  equations 
for  the  constants. 

It  is  obvious  that  these  two  formulas  may  also  be  used 


THE  POLAR1METER.  153 

to  determine  the  wave-length  of  light  by  solving  them  for  A. 
The  polarimeter  is  also  of  service  to  the  physical-chemist 
in  the  study  of  certain  problems  in  chemical  dynamics, 
such  as  the  rate  of  inversion  of  cane-sugar.  Its  use  in 
this  connection  will  be  explained  in  a  later  chapter.  The 
student  who  would  become  familiar  with  the  various  forms 
of  polarizing  apparatus  and. their  uses  is  referred  to  uDas 
optische  Drehungsvermogen 7;  by  Landolt  (English  transla- 
tion, "  The  Optical  Rotation  of  Organic  Substances/'  by  Long). 


ELECTRICAL  MEASUREMENTS. 


CHAPTER  IX. 

ELECTRICAL  UNITS. 


ELECTRICAL  energy,  as  well  as  every  other  form  of  energy, 
may  be  resolved  into  two  factors  —  a  capacity  factor  and  an 
intensity  factor,  or  the  electrical  energy 


where  e  is  the  capacity  factor  and  n  the  intensity  factor. 
The  capacity  factor  of  electrical  energy  is  the  coulomb,  while 
the  intensity  factor  is  the  volt. 

All  electrical  measurements  ultimately  resolve  them- 
selves into  the  determination  of  these  two  factors,  although 
we  frequently  arrive  at  the  result  through  the  measurement 
of  certain  derived  quantities  which  bear  to  them  well-known 
relations.  Of  these  relations  the  following  may  be  taken  as 
typical: 

E 

'-*  ........  « 

where  /  is  the  current  strength,  E  the  potential,  and  R  the 
resistance; 

/-J,    ........    (2) 

154 


ELECTRICAL   UNITS.  155 

where  /  has  the  same  significance  as  above  and  where  Q 

denotes  the  quantity  of  electricity  which  flows  in  the  time  T. 

From  relations  (1)  and  (2)  we  may  derive  the  following: 


Since  the  galvanometer  and  the  resistance-box  enable  us 
to  measure  current  strengths  and  resistances  with  compara- 
tive ease,  these  derived  magnitudes  assume  great  practical 
importance. 

The  following  definitions  of  practical  electrical  units  are 
taken  from  the  Proceedings  of  the  International  Electrical 
Congress  held  in  Chicago,  August  21,  1893: 

"  Resolved,  That  the  several  governments  represented  by 
the  de!egates  of  this  International  Congress  of  Electricians 
be,  and  they  are  hereby,  recommended  to  formally  adopt 
as  legal  units  of  electrical  measure  the  following: 

"  1.  As  a  unit  of  resistance,  the  international  ohm,  which 
is  based  upon  the  ohm  equal  to  109  units  of  resistance  of  the 
C.G.S.  system  of  electromagnetic  units,  and  is  represented  by 
the  resistance  offered  to  an  unvarying  electric  current  by  a 
column  of  mercury  at  the  temperature  of  melting  ice,  14.4521 
grams  in  mass,  of  a  constant  cross-sectional  area  and  of  the 
length  of  106.3  centimetres. 

"2.  As  a  unit  of  current,  the  international  ampere,  which  is 
one-tenth  of  the  unit  of  current  of  the  C.G.S.  system  of  elec- 
tromagnetic units,  and  which  is  represented  sufficiently  well 
for  practical  use  by  the  unvarying  current  which,  when 
passed  through  a  solution  of  nitrate  of  silver  in  water,  in 
accordance  with  accompanying  specification,  deposits  silver 
at  the  rate  of  0.001118  gram  per  second. 

"3.  As  a  unit  of  electromotive  force,  the  international 
volt,  which  is  the  E.M.F.  that  Lteadily  applied  to  a  conductor 


156  ELECTRICAL  MEASUREMENTS. 

whose  resistance  is  one  international  ohm  will  produce  a 
current  of  one  international  ampere,  and  which  is  repre- 
sented sufficiently  well  for  practical  use  by  ]f||  of  the  E.M.F. 
between  the  poles  or  electrodes  of  the  voltaic  cell  known  as 
Clark's  cell. 

"  4.  As  the  unit  of  quantity,  the  international  coulomb, 
which  is  the  quantity  of  electricity  transferred  by  a  current 
of  one  international  ampere  in  one  second.  .  .  . 

"  6.  As  the  unit  of  energy,  the  joule,  which  is  107  units 
of  work  in  the  C.G.S.  system  and  which  is  represented  suffi- 
ciently well  for  practical  use  by  the  energy  expended  in  one 
second  by  an  international  ampere  in  an  international  ohm." 

These  units  were  made  legal  by  Act  of  Congress  on 
July  12,  1894. 

Sources  of  Current.  —  By  far  the  best  source  of  current  for 
the  physico-chemical  laboratory  is  the  storage-cell.  Of  the 
several  forms  of  storage-cells  which  are  on  the  market  all  are 
based  upon  the  same  principle.  The  electrodes  consist  of 
two  lead  plates  or  grids  the  interstices  of  which  are  filled 
with  a  paste  of  lead  sulphate  made  by  mixing  one  of  the 
oxides  of  lead  with  dilute*  sulphuric  acid.  These  electrodes 
are  immersed  in  dilute  sulphuric  acid  and  a  current  is  sent 
through  the  cell.  The  chemical  changes  within  the  cell  are 
very  complex,  but  the  chief  action  of  the  current  consists  in 
the  liberation  of  hydrogen  at  one  electrode  which  reacts  with 
the  lead  sulphate,  forming  spongy  lead  and  sulphuric  acid, 
which  dissolves  ;  the  S04  ions  upon  reaching  the  other  elec- 
trode react  as  follows: 


PbS04+  S04+  2H20  =  Pb02+  2H2S04. 

The  sulphuric  acid  formed  dissolves,  while  the  lead  diox- 
ide remains  on  the  grid.  When  the  greater  part  of  the  lead 
sulphate  has  been  converted  into  metallic  lead  and  lead  diox- 


SOURCES  OF  CURRENT.  157 

ide  the  cell  is  "  charged/'  and  may  be  used  as  a  source  of 
current.  The  current  flows  in  the  opposite  direction  to  the 
charging  current  until  the  battery  is  discharged,  when  the 
charging  process  is  repeated.  The  storage  cell  is  remarkable 
for  its  efficiency,  nearly  80  per  cent,  of  the  energy  sup- 
plied in  charging  being  recovered  on  discharging. 

The  voltage  of  a  freshly  charged  accumulator  is  nearly 
2.5  volts,  which  gradually  falls  to  about  1.8  volts  as  the 
discharge  continues.  The  quantity  of  electricity  which  a 
storage-cell  can  furnish  is  approximately  0.04  ampere-hour 
for  each  square  centimetre  of  surface  of  lead  dioxide  ex- 
posed. An  accumulator  should  never  be  charged  or  dis- 
charged more  rapidly  than  0.01  ampere  per  square  centi- 
metre of  electrode  surface.  The  discharge  should  never  be 
continued  below  1.9  volts.  The  specific  gravity  of  the 
acid  solution  should  be  1.18;  this  will  fall  to  about  1.15  after 
discharge.  In  charging  the  battery  the  positive  pole  is 
connected  with  the  positive  pole  of  the  dynamo,  and  the 
negative  pole  with  the  negative  pole  of  the  dynamo,  a  variable 
resistance  being  introduced  so  that  the  strength  of  the  charg- 
ing current  may  be  altered  at  will.  The  charging  is  con- 
tinued until  there  is  a  vigorous  evolution  of  gas. 

The  lead-sulphate  paste  in  the  grids  suffers  considerable 
expansion  and  contraction  during  charge  and  discharge,  for 
which  reason  it  is  essential  always  to  charge  the  battery  in 
the  same  direction. 

The  grids  suffer  disintegration  after  a  time,  so  that  it  is 
necessary  to  renew  them. 

For  currents  of  lower  voltages  the  well-known  primary 
cells  of  Daniell  and  Le  Clanche  are  of  service. 

The  Daniell  cell,  which  is  designed  for  closed-circuit  work, 
furnishes  ordinarily  an  E.M.F.  of  1.08  volts,  and  remains 
constant  for  quite  a  period  of  time. 


158  ELECTRICAL  MEASUREMENTS. 

The  Le  Clanche  cell  is  intended  for  use  on  open  circuit; 
the  initial  E.M.F.  of  the  cell  varies  from  1.4  to  1.7  volts,  and 
the  internal  resistance  from  about  0.4  to  2.0  ohms.  Cells 
which  serve  as  standards  of  electromotive  force  will  be  con- 
sidered in  another  place. 


CHAPTER  X. 

RESISTANCE    (CONDUCTIVITY). 

THE  three  electrical  quantities  which  the  physical  chem- 
ist has  most  frequently  to  measure  are  resistance  or  its 
reciprocal,  conductivity,  current  strength,  and  electromotive 
force.  In  other  words,  the  three  quantities  involved  in 
the  equation 


Conductors  of  electricity  are  usually  divided  into  two 
classes,  though  there  is  much  doubt  as  to  whether  there  is 
any  true  distinction  between  them:  (1)  those  which  conduct 
the  current  without  suffering  chemical  decomposition,  and  (2) 
those  which  undergo  chemical  change  when  traversed  by  the 
electric  current.  To  the  first  class  belong  the  metals  and 
carbon,  while  to  the  second  belong  the  solutions  of  many 
substances  which  undergo  decomposition  at  the  poles.  It  is 
with  the  second  class  of  conductors  that  we  are  chiefly  con- 
cerned. 

These  conductors  are  known  as  electrolytes,  and  include 
chiefly  the  solutions  of  acids,  bases,  and  salts.  There  are 
many  substances  which  in  solution  do  not  conduct  the  elec- 
tric current,  and  these  are  known  as  non-electrolytes;  among 
these  may  be  mentioned  the  alcohols,  the  ketones,  and  the 
hydrocarbons. 

159 


160  ELECTRICAL  MEASUREMENTS. 

Specific  and  Molecular  Conductivity. — The  specific  re- 
sistance of  a  conductor  is  the  electrical  resistance  of  a  centi- 
metre cube  of  it  when  the  current  flows  through  it  from  one 
face  to  the  face  opposite.  Specific  resistance  is  wholly 
dependent  upon  the  nature  of  the  conductor.  Denoting  the 
specific  resistance  by  s',  and  the  length  and  cross-sectional 
area  of  the  conductor  by  I  and  a  respectively,  then  the  re- 
sistance is 

_s[Z 

or 

,     ra 

Since  conductivity  is  the  reciprocal  of  resistance,  it  follows 
that  the  specific  conductivity  of  the  conductor  is 

ra 

Conductors  of  the  second  class,  as  has  been  said,  consist  of 
solutions  of  an  electrolyte  in  some  solvent,  and  since  liquids 
have  no  definite  form  it  is  obvious  that  the  above  definition 
of  specific  conductivity  does  not  apply.  Since  the  conduc- 
tivity of  solutions  depends  upon  the  dissolved  electrolyte, 
we  select  the  gram-molecular  weight  of  dissolved  substance 
in  a  litre  as  the  basis  of  a  definition  which  shall  render  the 
resistances  of  all  solutions  comparable.  Consider  a  litre  of 
solution  containing  a  gram-molecular  weight  placed  between 
two  electrodes  which  are  separated  by  a  distance  of  1  cm. 
The  cross-section  will  be  1000  cm.2  This  will  have  T^Vir  the 
resistance  or  1000  times  the  conductivity  of  a  centimetre 
cube  of  the  same  solution. 

If  v  denotes  the  number  of  cubic  centimetres  of  any 
solution  containing  a  gram-molecule  of  dissolved  substance, 


RESISTANCE  (CONDUCTIVITY)  161 

and  s  represents  the  specific  conductivity  of  a  centimetre 
cube  of  the  solution,  the  molecular  conductivity  /*  is 

P  =  vXs  ........     (1) 

Where  g  gram-molecules  of  dissolved  substance  are  con- 
tained in  a  litre  of  solution,  we  have  as  a  perfectly  general 
expression 


If  the  specific  conductivity  be  referred  to  a  cylinder  of 
solution  100  cms.  in  length  and  0.01  cm2  in  cross-section, 
then  obviously  (1)  and  (2)  become 

......     (3) 

-     (4) 


If  in  (I)'  v  denote  the  volume  in  cubic  centimeters  which 
contains  1  gram-equivalent  of  solute,  then  the  equivalent 
conductivity,  A?  is 

A-vXs  .........     (5) 

The  molecular  or  equivalent  conductivities  of  solutions 
are  thus  seen  to  be  the  conductivities  of  comparable  quan- 
tities of  different  solutes. 

Resistance-boxes.  —  In  the  measurement  of  the  resistance 
^f  electrolytes,  as  in  the  measurement  of  other  resistances,  it 
is*  necessary  to  have  a  series  of  known  resistances  the  values 
oi  which  have  been  determined  with  great  accuracy.  Such 
a  series  of  resistances  is  to  be  had  in  the  ordinary  resistance- 
box  (Fig.  62).  This  consists  of  a  series  of  coils  of  insulated 
wire  wound  double  upon  spools  in  order  to  avoid  self-induction 
on  starting  or  stopping  the  current.  Each  coil  is  exactly 
adjusted  to  give  the  desired  resistance  and  then  is  fastened 
to  the  under  side  of  the  hard-rubber  cover  of  the  box.  Its 
ends  are  soldered  to  two  heavy  copper  rods  which  pass  through 
the  cover  and  are  connected  to  the  heavy  brass  blocks  upon 
the  top  of  the  cover  of  the  box.  The  several  coils  are  con- 


162  ELECTRICAL  MEASUREMENTS. 

nected  in  series  by  the  insertion  of  accurately  fitting  brass 
plugs  in  the  holes  between  the  segments  of  brass  upon  the 
cover.  Thus  when  any  plug  is  withdrawn  the  current  must 
traverse  the  coil  which  bridges  the  gap  between  the  dis- 
connected brass  blocks.  Opposite  each  hole  upon  the  cover 
is  marked  the  resistance  of  the  underlying  coil.  The  coils 
are  usually  adjusted  to  the  following  resistances  in  ohms: 
1,  2,  2,  5,  10,  10,  20,  50,  100,  100,  200,  500,  1000,  2000,  2000, 
5000,  making  a  total  of  11,000  ohms  in  the  box.  Each  box  is 


FIG.  62. 

adjusted  to  some  convenient  temperature,  which  is  marked 
upon  the  cover  of  the  box.  Should  the  room  temperature 
vary  from  that  for  which  the  box  is  adjusted,  corrections 
may  be  introduced  provided  the  temperature  coefficient  of 
the  wire  from  which  the  coils  are  wound  is  known.  For 
manganin  wire  the  temperature  coefficient  ranges  from 
+0.00001  to  +0.00004. 

The  plugs  of  a  box  should  fit  very  exactly  in  their  conical 
sockets,  and  care  should  be  taken  to  insure  the  plugs  being 
clean  and  free  from  oxide.  This  is  accomplished  by  rubbing 
them  with  a  cloth  dipped  in  a  very  weak  solution  of  oxalic 
acid;  grease  may  be  removed  by  washing  them  with  alcohol 
and  ether. 


M31STANCE  (CONDUCTIVITY). 


163 


"•"n  inserting  the  plugs  too  great  pressure  should  not  be 
applied,  otherwise  there  is  danger  of  breaking  the  rubber 
tops  upon  removal.  The  actual  resistance  through  a  plug 
when  it  is  well  cleaned  and  firmly  seated  is  from  0.00005  to 
D.0001  ohm. 

A  good  resistance-box  should  be  protected  when  not  in  use 
by  a  light  wooden  box. 

When  in  use  care  should  be  taken  that  direct  sunlight 
does  not  fall  on  the  box,  neither  should  it  be  used  in  a  room 
where  corrosive  fumes  are  liable  to  be  liberated. 

Wheatstone's  Bridge. — For  the  measurement  of  all  but 
high  or  very  low  resistances  the  Wheatstone's  bridge 


is  the  most  convenient.  It  consists  of  a  combination  of 
resistances,  as  shown  in  Fig.  63.  It  is  obvious  that  in  the 
divided  circuit  from  C  to  A  there  must  be  a  point  on  the 
branch  CD  A  which  will  have  the  same  potential  as  a  point 
on  the  branch  CEA.  Let  us  imagine  that  by  means  of  the 
galvanometer  G  two  such  points  have  been  found,  and  let 


164  ELECTRICAL  MEASUREMENTS. 

these  points  be  denoted  by  D  and  E.    Then  we  have  the 
following  proportion: 

R  :Z=r3:r4, 
or 

Rr4=Xr3. 

From  this  equation  it  is  evident  that  if  the  values  of  any 
three  of  the  four  resistances  are  known  the  other  one  is  deter- 
mined. 

Let  us  imagine  the  resistance-box  to  be  inserted  in  the 
arm  R  and  the  unknown  resistance  to  be  placed  in  the  arm  X\ 
then  we  can  alter  the  position  of  the  point  E  until  the  galvan- 
ometer shows  no  deflection,  and  thus  determine  the  lengths 
of  CE  and  AE.  Since  resistance  is  directly  proportional  to 
the  length  of  the  conductor,  it  follows  that  the  values  of  r3 
and  r4  are  proportional  to  the  lengths  AE=^  and  CE=12)  or 


The  most  convenient  form  of  the  Wheatstone  's  bridge  is 
the  slide-  wire-metre  bridge,  Fig.  64.  'In  this  form  of  bridge 


FIG.  64. 

(Fig.  65)  the  conductor  AEC,  corresponding  to  the  similarly 
lettered  portion  of  Fig.  63,  is  made  of  a  thin  uniform  wire 
one  metre  long,  the  point  E  being  determined  by  a  sliding 
contact  which  moves  over  a  millimetre  scale.  The  arms 
CD  and  DA  of  the  bridge  consist  of  heavy  copper  straps 
which  offer  inappreciable  resistance.  The  lettering  in  the  two 
diagrams  being  the  same,  the  latter  becomes  self-explana- 
tory. A  single  determination  of  the  position  of  the  index  is  not 


RESISTANCE  (CONDUCTIVITY). 


165 


reliable  owing  to  variations  in  the  size  of  the  wire  and  to  lack 
of  precision  in  determining  the  point  of  balance.  For  these 
reasons  the  mean  of  a  series  of  observations  should  be  taken. 
When  a  direct  current  is  passed  through  the  solution  of 
an  electrolyte  bubbles  of  gas  appear  on  the  electrodes 
after  a  very  short  time,  or,  as  we  say,  polarization  sets  in. 
Polarization  causes  a  counter  E.M.F.,  which  makes  the  ac- 
curate measurement  of  conductivity  an  impossibility.  This 


difficulty  has  been  overcome  by  Kohlrausch,  who  introduced 
the  use  of  the  alternating  current.  The  alternating  current 
is  furnished  by  a  small  inductorium,  the  wires  from  the  sec- 
ondary of  which  are  connected  with  the  ends  of  the  bridge- 
wire.  Since  the  galvanometer  cannot  be  used  with  the 
alternating  current,  it  is  replaced  by  a  telephone.  The 
inductorium  is  best  placed  in  another  room  from  that,  in 
which  the  bridge  is  placed,  so  that  the  sound  of  the  coil  can 
only  be  heard  through  the  telephone.  The  sliding  contact 
is  then  moved  along  the  bridge-wire  until  a  point  is  found 


166  ELECTRICAL  MEASUREMENTS. 

where  the  sound  of  the  coil  either  entirely  vanishes  or  attains 
a  minimum  of  intensity.  This  point  is  the  position  of  bal- 
ance between  the  arms  of  the  bridge.  A  very  convenient 
form  of  telephone  is  that  shown  in  Fig.  66,  where  the  ear- 


FIG.  66. 

piece  can  be  held  to  the  ear  by  means  of  the  elastic  metal 
strap  which  encircles  the  head. 

Before  the  Wheatstone's  bridge  is  used  the  wire  should 
be  carefully  calibrated.  Of  the  several  methods  in  use  for 
this,  that  of  Strouhal  and  Barus  is  best  adapted  to  the 
physico-chemical  laboratory. 


RESISTANCE   (CONDUCTIVITY). 


167 


Calibration  of  the  Bridge-wire. — The  method  of  calibra- 
tion usually  employed  is  that  of  Strouhal  and  Barus.  Ten 
approximately  equal  resistances  of  German-silver  wire  are 
prepared  by  soldering  to  the  ends  of  each  length  of  wire  a 
short,  heavy  copper  wire  which  is  afterward  amalgamated. 
The  lengths  of  the  resistances  should  be  so  chosen  that  the 
sum  of  all  of  the  resistances  should  nearly  equal  the  resistance 
of  the  manganin  bridge-wire.  Upon  a  narrow  strip  of  wood 
which  is  placed  parallel  to  the  bridge-wire  are  placed  nine 
mercury-cups,  11  cm.  from  centre  to  centre.  The  ten  re- 


Mi    M2 


FIG.  67. 

sistances  are  then  arranged  in  them  as  shown  in  Fig.  67,  and 
the  connections  made  as  indicated. 

We  first  find  a  point  M1  on  AC  which  has  the  same 
potential  as  Nly  this  being  accomplished  by  means  of  a  sen- 
sitive galvanometer,  G.  In  like  manner  a  point  M2  is 
found  having  the  same  potential  as  N2.  The  wires  I  and  II 
are  now  interchanged,  and  points  M'2  and  M3  are  found 
which  have  the  same  potentials  as  N2  and  N3.  The  calibra- 
tion distances  should  slightly  overlap,  that  is,  the  resistance 
of  I  should  be  so  chosen  that  the  reading  for  M2,  M3 .  . .  shall 


168  ELECTRICAL  MEASUREMENTS. 

be  a  little  greater  than  the  reading  for  M'2,  M J . . .  Now 
I  and  III  are  interchanged,  and  the  same  operations  us 
before  are  repeated.  In  this  way  the  process  is  continued 
until  I  has  replaced  each  resistance  in  succession,  finally 
taking  the  place  of  the  last  one.  In  this  way  we  have  deter- 
mined ten  divisions  of  the  wire  of  equal  resistance,  each 
division  being  nearly  one-tenth  of  the  whole. 

The  ten  values  are  added  together  and  the  sum  sub- 
tracted from  100  cm.,  the  length  of  the  bridge-wire.  This 
difference  is  divided  by  10  and  each  length  is  corrected  by 
this  amount,  thus  making  the  sum  100  cm. 

By  adding  the  parts  we  obtain  the  points  which  corre- 
spond to  tenths  of  the  wire,  and  the  differences  between 
these  and  the  decimetre  divisions  give  the  corrections  to  be 
applied.  Suppose  that  the  sum  of  the  first  three  lengths 
is  29.87,  then  the  correction  is  30.0-2987  =  4-0.13,  The 
telephone  may  be  used  in  place  of  the  galvanometer,  but 
the  results  are  not  as  accurate  owing  to  the  uncertainty  as  to 
the  position  of  the  minimum.  Should  the  telephone  be  used, 
it  must  be  remembered  that  it  is  not  advisable  to  try  to  find 
the  position  of  exact  silence,  but  to  find  two  points  on  each 
side  of  the  position  of  minimum  sound  where  the  tones  are  of 
the  same  intensity.  These  two  positions  should  not  be  more 
than  a  centimetre  apart.  The  position  of  balance  then  lies 
half-way  between  these  two  points. 

Conductivity  Cells. — The  form  of  cell  to  be  used  in  the 
measurement  of  the  conductivity  of  solutions  depends 
largely  upon  the  nature  of  the  solution  to  be  investigated. 
For  solutions  of  low  conductivity,  cells  must  be  used  in 
which  the  electrodes  are  near  together,  while  in  the  study  of 
solutions  of  high  conductivity  it  is  essential  that  the  elec- 
trodes be  far  apart. 

In  most  cases  the  solutions  with  which  we  have  to  deal 


RESISTANCE   (^CONDUCTIVITY). 


16S 


are  dilute,  and  for  such  solutions  the  cell  suggested  by  Arrhe- 
nius  is  best  adapted  to  our  purpose.  This  cell  is  shown  in 
Fig.  68.  It  consists  of  two  circular  parallel  platinum  electrodes 
suspended  in  a  tall  cylindrical  glass  cup,  the  cup  being  cov- 
ered with  a  well-fitting  ebonite  cover.  The  electrodes  are 


FIG.  68. 


made  of  thick  platinum  foil  about  4  cm.  in  diameter.  Each 
electrode  is  welded  at  its  centre  to  a  short,  thick  piece  of 
platinum  wire,  each  wire  being  sealed  into  a  glass  tube  by 
means  of  fusible  enamel  glass.  The  electrodes  are  held  in 
the  desired  position  by  being  fastened  into  the  ebonite  cover 
by  means  of  sealing-wax.  The  solution  to  be  examined  is 


170  ELECTRICAL  MEASUREMENTS. 

placed  in  the  cell  ro  as  to  cover  the  upper  electrode. 
The  electrodes,  which  ihould  fit  the  cms-tection  of  the  cup 
as  nearly  as  possible,  are  held  in  position  by  the  ebonite  cover, 
in  the  under  side  of  which  is  cut  a  circular  groove  which  fits 
accurately  over  the  edge  of  the  cup.  The  glass  tubes  are 
filled  with  mercury,  and  by  means  of  bent  copper  wires  dip- 
ping into  this,  electrical  connection  is  established. 

In  order  to  insure  a  sharp  minimum  in  the  telephone, 
the  electrodes  must  be  thoroughly  covered  with  platinum- 
black.  The  platinizing  is  best  accomplished  by  filling  the 
cell  with  "platinizing  solution"  (3  grams  PtCl4,  0.03  gram 
Pb(C2H302)2  in  100  grams  of  water)  and  passing  a  current  of 
4-5  volts,  with  frequent  changes  in  direction,  until  both 
electrodes  are  covered  with  a  fine  velvety  coating  of  platinum- 
black.  After  platinizing  they  are  carefully  washed,  and  then 
a  dilute  solution  of  sodium  hydroxide  is  placed  in  the  cell, 
the  plates  inserted,  and  the  current  passed  for  a  few  mo- 
ments. This  procedure  is  to  insure  the  removal  of  any  of 
the  chlorine  which  may  have  been  retained  by  the  platinum- 
black.  The  sodium  hydroxide  is  then  removed  by  washing 
with  dilute  hydrochloric  acid,  and  the  acid  is  removed  by 
thorough  washing  with  pure  distilled  water. 

Since  it  is  absolutely  essential  that  the  temperature  of 
the  cell  contents  remain  at  a  definite  temperature,  the  cell  is 
placed  in  a  thermostat-bath.  The  cell  is  held  on  a  metal  or 
ebonite  shelf  which  is  fastened  to  the  edge  of  the  bath,  Fig.  71. 
Around  the  cell  there  is  a  tight-fitting  ebonite  ring  which 
keeps  the  cell  from  slipping  through  the  hole  in  the  shelf. 
Two  mercury-cups  upon  the  shelf  serve  to  make  electrical 
connection  between  the  cell  and  the  wires  to  the  bridge. 

The  following  illustrations,  Figs.  72-75,  show  other  forms 
of  conductivity  cells,  each  bein>;  des'gned  to  meet  special 
requirements.  When  it  is  desired  to  protect  the  solvent  from 


RESISTANCE  (CONDUCTIVITY). 


171 


the  moisture  of  the  air  the  forms  shown  in  Figs.  76  and  77 
may  be  used. 

Induction  Coil  and  Telephone. — The  induction  coil  should 
be  small  and  the  hammer  of  the  make  and  break  should  be 
light  and  capable  of  rapid  vibration. 

A  single  lead  accumulator  or  a  dry  cell  may  be  used  to 
operate  the  coil  and  a  variable  resistance  should  be  included 
in  the  circuit,  so  that  the  strength  of  the  current  may  be  so 
altered  as  to  just  secure  continuous  vibration  of  the 
hammer. 

A  form  of  coil  specially  designed  for  measuring  the  con- 
ductivity of  solutions  is  shown  in  Fig.  69. 


FIG  69. 

The  variable  resistance  consists  of  a  wire  wound  spirally 
around  the  drum  C,  contact  being  made  by  means  of  the 
screw  D. 

The  coil  is  shown  at  A  and  the  vibrator  at  B.  In  Fig.  70 
the  details  of  the  vibrator  are  shown. 


172 


ELECTRICAL  MEASUREMENTS. 


In  the  coil  shown  in  Fig.  69,  the  base  rests  on  a  pad  of 
felt  FF,  thus  deadening  the  sound  of  the  vibrator. 


(   \ 


] 


CD 


FIG.  70. 


A  convenient  form  of  telephone  is  the  small  ear-piece, 
such  as  is  shown  in  Fig.  66.    It  is  of  importance,  however, 


FIG.  71. 


FIG.  72. 


to  have  a  telephone  of  high  sensitiveness  if  accurate  results 
are  to  be  obtained. 


RESISTANCE  (CONDUCTIVITY}. 


173 


Resistance  Capacity  of  the  Cell. — As  has  been  pointed 
cut,  the  conductivity  of  an  electrolyte  is  expressed  as  molecu- 
lar conductivity,  which  is  the  conductivity  of  a  gram-molecu- 
lar weight  of  the  electrolyte  or  the  conductivity  of  the  volume 
of  solution  containing  a  gram-molecular  weight  when  placed 


FIG.  73. 


JiQ.  74. 


FIG.  75. 


between  two  electrode  which  are  I  <wn,  apart.    This  relation  is 
expressed  thus: 

JJ.=VS. 

Now  the  conductivity  as  measured  in  a  cell  stands  to  the 
specific  conductivity  in  a  ratio  which  is  dependent  upon  the 
shape  and  size  of  both  electrodes  and  cell.  This  factor  K 
has  been  called  by  Kohlrausch  the  resistance  capacity  of 
the  cell.  To  determine  K  for  any  cell,  a  solution  of  known 
specific  conductivity  is  measured  and  the  ratio  of  the  specific 
conductivity  to  the  observed  conductivity  is  the  resistance 
capacity.  If  C  is  the  observed  conductivity  of  a  solution  of 
which  the  specific  conductivity  is  s,  then 


174 


ELECTRICAL  MEASUREMENTS. 


If  C"  is  the  conductivity  of  another  solution  having  a 
specific  conductivity  s',  then 


By  reference  to  the  notation  in  Fig.  78,  where  the  complete 
connections  of  the  bridge  for  a  conductivity  measurement  are 


h 


X 


FIG.  76. 


FIG.  77. 


shown,  the  following  equation  will  be  seen  to  be  in  accordance 
with  the  law  of  Wheatstone's  bridge: 


but 


s=KC, 


hence 
Since 


RESISTANCE  (CONDUCTIVITY). 


K  a 
w  b' 


175 


v  a 

--r. 

w  b 


Since  potassium  chloride  can  be  obtained  in  u  very  pure 
state  by  repeated  crystallization,  it  is  most  usually  employed 
in  determining  the  value  of  K. 


FIG.  78. 


N 


A  -rrr  solution  of  KC1  has  been  found  to  have  a  molecular 

conductivity  of  129.7  at  25°  C.  or  112.2  at  18°  C,  This  solu- 
tion contains  74.59  grams  of  KC1  in  50  litres  of  solution. 
The  value  of  K  is  then  found  from  the  formula 

bw 


or  at  25°  C. 


£=129.7=2.594^ 


176  ELECTRICAL  MEASUREMENTS. 

Carrying  out  a  Measurement. — As  a  typical  example  of  a 
conductivity  measurement  we  may  take  the  experimental 
determination  of  K. 

The  one-fiftieth  normal  potassium  chloride  solution  is 
poured  into  the  carefully  cleaned  cell,  and  the  electrodes  are 
inserted,  care  being  taken  to  avoid  air-bubbles  clinging  to 
the  plates.  The  cell  is  then  placed  in  the  thermostat-bath, 
which  is  brought  exactly  to  25°  C.  After  the  cell  has  re- 
mained in  the  bath  a  sufficient  length  of  time  for  the  solution 
to  acquire  a  uniform  temperature  throughout  of  25°  the  cell 
is  connected  with  the  circuit,  the  switch  thrown  in,  and  by 
means  of  the  variable  resistance  the  point  of  minimum  tone 
is  brought  near  the  middle  of  the  bridge. 

The  resistances  in  the  box  should  never  be  less  than  20 
ohms,  since  the  telephone  method  is  not  accurate  for  smaller 
resistances.  It  can  be  shown  that  the  bridge  readings 
between  40  cm.  and  60  cm.  are  the  most  accurate,  so  that  it 
should  be  made  a  rule  to  try  to  bring  the  point  of  balance 
between  these  limits.  Several  readings  should  be  taken 
with  different  resistances  in  the  box. 

By  substituting  these  values  in  the  equation 

K  =2.594^ 
a 

the  value  of  the  resistance  capacity  of  the  cell  is  found.  In 
carrying  out  other  conductivity  measurements  the  procedure 
is  the  same,  but  the  value  sought  is  that  of  the  molecular  con- 
ductivity,' K  having  been  determined  for  the  cell  used.  The 
results  are  then  substituted  in  the  equation 

v   v    a 

U.=K r-. 

w  b 

A  table  has  been  compiled  by  Obach  whereby  the  ratio 
of  a  to  b  is  given  for  a  wire  100  cm.  in  length.  This  is  very 


RESISTANCE  (CONDUCTIVITY).  177 

useful  where  many  conductivity  measurements  are  to  be 
made. 

Since  the  cell  is  to  be  ueed  for  a  series  of  measurements, 
it  is  obvious  that  the  electrodes  must  not  be  moved  with 
respect  to  each  other,  nor  must  their  surfaces  be  altered  in 
any  way.  They  should  be  cleaned  with  pure  distilled  water, 
and  dried  by  washing  with  alcohol  and  ether.  When  not  in 
use  the  electrodes  should  be  suspended  in  an  appropriate 
rack  and  protected  from  the  dust.  The  distance  between 
the  electrodes  should  be  varied  according  to  the  concentration 
of  the  solution.  For  solutions  of  greater  concentration  than 

N 
x^  the  electrodes  should  be  at  least  1  cm.  apart. 


In  making  conductivity  measurements  every  possible 
precaution  must  be  taken  to  insure  clean  and  well-made 
connections,  and  to  exclude  impurities  from  the  solutions. 

Pure  Water.  —  Since  most  conductivity  measurements 
are  made  upon  aqueous  solutions,  it  becomes  of  importance 
to  secure  the  purest  water  possible  for  making  the  solutions. 

By  distilling  in  vacuo  the  purest  water  obtained  by 
other  methods  of  distillation,  Kohlrausch  succeeded  in  pre- 
paring water  having  a  specific  conductivity  in  vacuo  of 
D.04X10-6. 

This  degree  of  purity  cannot  be  attained  in  ordinary 
practice. 

Nernst  has  proposed  purifying  the  water  for  conductivity 
purposes  by  fractional  crystallization. 

Far  more  rapid  and  efficient  is  the  method  employed  by 
H.ulett.  This  consists  in  first  distilling  ordinary  distilled 
water  from  potassium  dichromate  and  sulphuric  acid,  and 
then  redistilling  from  a  solution  of  barium  hydroxide.  In 
this  way  it  is  possible  to  obtain  water  having  a  specific  con- 
ductivity of  from  0.7  X  10~6  to  0.8  X  10~fl.  Jones  and  Mackay 


178  ELECTRICAL  MEASUREMENTS. 

have  improved  Hulett's  process,  so  that  the  distillation 
from  dichromate  of  potassium  and  sulphuric  acid  and  from 
barium  hydroxide  becomes  perfectly  continuous.  In  this  way 
four  or  five  litres  of  water  having  a  specific  conductivity  of 
2xlO~6  can  be  obtained  daily. 

In  calculating  the  molecular  conductivity  of  neutral 
substances  a  deduction  must  be  made  for  the  conductivity 
of  the  water. 

This  calculation  is  performed  by  multiplying  the  spe- 
cific conductivity  of  the  water  by  the  molecular  volume  of 
the  solution  and  subtracting  the  product  from  the  molecular 
conductivity.  This  correction  need  only  be  applied  to  solu- 

N 
tions  less  than  ^,  since  for  greater  concentrations  the  cor- 

rection is  much  less  than  the  experimental  error.  With 
acids  and  bases  the  impurities  present  in  the  water  are  like'y 
to  neutralize  the  acid  or  the  base,  thus  causing  a  diminution 
in  the  conductivity.  It  is  at  once  evident  that  the  applica- 
tion of  any  correction  in  such  cases  would  be  absurd. 

Equivalent  Conductivity.  —  Frequently  the  results  of 
conductivity  measurements  are  expressed  as  equivalent 
conductivities  instead  of  molecular  conductivities.  Equiva- 
lent conductivity  is  derived  from  molecular  conductivity  by 
dividing  it  by  the  valence.  Thus  the  equivalent  conductiv- 
ity of  NaN03  is  the  same  as  the  molecular  conductivity,  the 
equivalent  conductivity  of  BaCl2  is  equal  to  one-half  of  the 
molecular  conductivity,  and  in  A12(S04)3  the  equivalent  is 
one-sixth  of  the  molecular  conductivity. 

Denoting  equivalent  conductivity  by  A,  we  have 


where  n  is  the  number  of  equivalents  contained  in  a  litre. 


RESISTANCE  (CONDUCTIVITY).  179 

Degree  of  Dissociation.  —  It  is  obvious  that  the  degree  of 
dissociation  is  the  ratio  of  the  molecular  conductivity  at  any 
dilution  to  the  molecular  conductivity  at  infinite  dilution, 
for  at  moderate  dilutions  the  molecules  are  only  partially 
broken  down  into  ions,  while  at  infinite  dilution  ionization  is 
complete.  The  degree  of  dissociation  a  is  then  expressed 
thus: 


a= 


The  value  of  p^  is  determined  by  measuring  the  conductiv- 
ities of  successive  dilutions  until  the  molecular  conductivity 
remains  constant,  showing  that  the  e!ectrolyte»  is  completely 
dissociated. 

The  Dissociation  Constant.  —  Many  monobasic  organic 
acids  and  other  slightly  dissociated  electrolytes  exhibit  a 
variation  of  molecular  conductivity  with  change  in  volume. 
The  mathematical  expression  of  this  relation  is 


where  k  is  a  constant,  known  as  the  dissociation  constant. 
It  is  customary  to  express  the  dissociation  constant  for  an 
acid  as  one  hundred  times  the  value  given  by  the  above 
equation,  thus  avoiding  too  small  numbers,  or  K  =  100&.  In 
measuring  the  dissociation  constant  of  an  acid  we  proceed  in 
the  following  manner :  The  strength  of  the  acid  is  first  deter- 
mined by  means  of  a  relation  of  standard  alkali,  care  being 
taken  that  the  acid  is  not  stronger  than  tenth-normal.  A 
thoroughly  cleaned  bottle  of  250  c.c.  capacity  is  filled  with 
the  purest  conductivity  water,  and  is  immerred  to  the  neck 
in  the  thermostat  bath,  which  is  adjusted  to  25°  C. 

An  Arrhenius  conductivity  cell  is  then  filled  with  10  c.c. 


180  ELECTRICAL  MEASUREMENTS. 

of  the  approximately  N/10  acid,  a  pipette  calibrated  to 
deliver  being  used.  The  electrodes  are  then  inserted,  care 
being  taken  to  avoid  air-bubbles,  and  the  cell  is  placed  in 
the  thermostat  where  it  is  allowed  to  remain  for  about 
thirty  minutes,  when  it  will  have  acquired  the  temperature 
oL  the  bath.  The  conductivity  of  the  acid  is  then  measured. 
By  means  of  the  pipette  graduated  to  deliver,  10  cc.  of  water 
at  25°  are  removed  from  the  250-cc.  bottle  and  introduced 
into  the  cell,  the  solution  being  rendered  homogeneous  by 
slowly  raising  and  lowering  the  cover  and  electrodes.  After 
five  minutes  another  measurement  is  made.  With  a  pipette 
graduated  to  contain,  10  cc.  of  the  solution  in  the  cell  k 
removed  and  10  cc.  of  water  added  from  the  delivery  pipette. 
The  cell  is  allowed  to  remain  in  the  thermostat  for  five 
minutes,  when  another  measurement  is  made.  This  process 
is  continued  until  the  dilution  becomes  too  great  to. permit 
of  accurate  determinations. 

This  point  is  reached  when  the  dilution  becomes  about 
1000  or  1  gram-molecule  of  solute  in  1000  liters. 

Since  weak  acids  are  only  very  slightly  dissociated,  the 
determination  of  ^  is  accomplished  by  the  indirect  method 
of  measuring  the  molecular  conductivity  of  the  sodium 
salt. 

For  the  more  complex  acids  the  value  of  /^  may  be 
estimated  with  sufficient  accuracy  from  the  number  of  atoms 
in  the  molecule,  thus  avoiding  the  experimental  determination. 
The  following  table  gives  the  value  of  /^  at  25°  C.  for  com- 
plex acids  with  different  numbers  of  atoms : 

Acids  with  12  atoms /^  =383 

"     15    "     ^=380 

"      18    "     ^=378 

"     22    "     /^=376 

"     25    "      -...^=375 

"     30    " /< 


RESISTANCE  (CONDUCTIVITY).  181 

The  Basicity  of  Acids.  —  Ostwald  discovered  the  purely 
empirical  relation  that  one-tenth  of  the  difference  between 
the  molecular  conductivities  of  the  sodium  salt  of  an  organic 
acid  at  dilutions  32  and  1024  is  equal  to  the  basicity  of  the 
acid.  This  may  be  represented  thus  :  /*1024  —  ;*32  =  10  X  basicity. 

N 
About  20  c.c.  of  a  ^  solution  of  pure  sodium  hydroxide  is 

oZ 

titrated  with  the  dry  acid  of  which  the  basicity  is  sought, 
phenolphthalein  being  used  as  an  indicator.  When  the  pink 

N 
color  has  just  been  destroyed  the  ^  solution  of  the  sodium 

oZ 

salt  of  the  acid  is  placed  in  a  conductivity  cell  and  the  molecu- 
lar conductivity  determined.  The  solution  is  then  diluted 
with  pure  water  to  volume  1024  and  the  molecular  conductiv- 
ity again  determined.  The  difference  between  the  molecular 
conductivity  at  volume  1024  and  the  molecular  conductivity 
at  volume  32  divided  by  10  gives  the  basicity  of  the  acid. 

Solubility  by  the  Conductivity  Method.  —  The  saturated 
solution  of  a  difficultly  soluble  salt  may  be  considered  as 
completely  dissociated  since  the  solution  is  so  dilute.  We 
may  therefore  equate  /^  and  u^  and  write  the  equation  for 
molecular  conductivity  thus: 


v   a 


or  v 

wb 


where  v  is  the  number  of  litres  in  which  one  gram-molecule  of 
the  salt  is  dissolved. 

The  finely  powdered  difficultly  soluble  salt  is  well  washed 
with  pure  conductivity  water,  the  salt  being  then  brought 
into  the  conductivity  cell  and  covered  with  the  pure  water  of 
which  the  conductivity  is  known.  The  contents  of  the  cell  are 


182  ELECTRICAL  MEASUREMENTS. 

well  shaken,  the  electrodes  introduced,  and  the  whole  placed 
in  the  thermostat.  After  sufficient  time  has  elapsed  for  the 
cell  and  contents  to  acquire  the  temperature  of  the  bath  the 
conductivity  is  measured.  This  process  is  repeated  until 
constant  conductivity  is  obtained.  If  s  denotes  the  meas- 
ured specific  conductivity  of  the  solution  minus  the  specific 
conductivity  of  the  water,  and  XA  and  Ac  are  the  equivalent 
conductivities  of  the  anions  and  cations,  then  the  equiva- 

lent concentration   per  litre  is   A.  r  ',  a  formula  which  can 


be  readily  reconciled  with  the  preceding. 

The  conductivity  method  is  also  applicable  to  the  deter- 
mination of  the  concentration  of  solutions  of  electrolytes  and 
to  the  appproximate  determination  of  small  quantities  of 
electrolytes  in  mixtures  or  solutions  with  larger  quantities  of 
substances  having  lower  conductivity. 

For  further  information  on  the  conductivity  method 
the  student  is  referred  to  "  Das  Leitvermogen  der  Elektro- 
lyte,"  by  Kohlrausch  and  Holborn. 


CHAPTER  XI. 

ELECTROMOTIVE  FORCE. 

Clark  Standard  Cell. — In  accordance  with  the  decision  of 
the  International  Congress  of  Electricians  held  in  Chicago 
in  1893,  the  Clark  cell  has  been  made  the  legal  standard 
of  electromotive  force.  The  cell  consists  of  the  system 

-    Zn     ZnS04  |  Hg2S04 1  Hg  |  +. 


FIG.  79. 

Several  forms  of  this  cell  have  been  devised,  but  perhaps  the 
most  suitable  for  physico-chemical  purposes  is  the  Carhart- 

183 


184  ELECTRICAL  MEASUREMENTS. 

0!ark  cell,  which  has  the  advantages  of  both  portability 
and  a  lower  temperature  coefficient  than  the  normal  Clark 
cell.  The  arrangement  of  this  cell  is  shown  in  Fig.  79. 

Into  the  bottom  of  a  glass  tube  5  cm.  long  and  1.5  cm. 
in  diameter  is  sealed  a  piece  of  No.  28  platinum  wire.  In 
contact  with  this  wire  is  pure  redistilled  mercury.  Upon 
this  there  is  a  layer  about  1  cm.  thick  of  pure  neutral  mer- 
curous  sulphate  mixed  with  neutral  zinc  sulphate  saturated 
at  0°  C.  This  paste  is  then  covered  with  a  layer  of  purified 
asbestos  upon  which  rests  the  electrode  of  pure  zinc  cast  as 
shown  in  the  figure.  To  the  top  of  the  zinc  is  soldered  a 
thin  copper  wire.  The  zinc  electrode  passes  through  a  thin 
disc  of  cork  which  holds  the  seal.  This  cork  must  be  boiled 
for  some  time  in  distilled  water  to  remove  the  tannin,  then 
dried,  and  finally  saturated  with  paraffin.  The  zinc  sulphate 
solution  which  surrounds  the  zinc  is  introduced  by  means  of  a 
funnel  before  the  zinc  is  inserted.  The  cell  is  finally  sealed 
by  running  in  a  hot  cement  of  gutta  percha  and  Burgundy 
pitch  with  enough  balsam  of  fir  to  impart  fluidity. 

Preparation  of  Materials.* — (a)  Mercury. — The  mercury 
should  first  be  purified  by  causing  it  to  pass  in  a  fine  stream 
through  a  long  column  of  dilute  nitric  acid  and  then  distilled 
in  a  vacuum. 

(b)  Zinc. — Only   the   purest   redistilled   zinc   should   be 
employed  in  making  the  zinc  electrode. 

(c)  Mercurous  Sulphate. — Mix  the  purest  obtainable  mer- 
curous  sulphate  with  a  small  quantity  of  pure  mercury,  and 
wash  the  whole  thoroughly  by  agitation  in  a  bottle ;  drain  off 
the  water  and  repeat  several  times.     After  the  last  washing 
drain  off  as  much  of  the  water  as  possible,  but  DO  NOT  DRY  BY 

HEATING. 

(d)  Zinc  Sulphate  Solution. — Prepare  a  neutral  saturated 

*  Taken  from  Carhart's  Electrical  Measurements. 


ELECTROMOTIVE  FORCE.  185 

solution  of  pure  recrystallized  zinc  sulphate  by  mixing  dis- 
tilled water  with  approximately  twice  its  weight  of  crystals 
of  the  salt,  and  adding  zinc  oxide  in  the  proportion  of  about 
2  per  cent,  by  weight  of  the  zinc  sulphate  crystals  to  neu- 
tralize any  free  acid  which  may  be  present.  The  crystals 
should  be  dissolved  by  heating  slightly,  but  the  solution  must 
not  be  warmed  above  30°  G.  Mercurous  sulphate  purified 
as  in  (c)  is  added  in  the  proportion  of  about  12  per  cent,  by 
weight  of  the  zinc  sulphate  crystals  to  neutralize  the  free 
zinc  oxide  remaining.  The  solution  is  then  filtered  and 
cooled  to  0°.  Crystals  should  form  as  the  solution  cools. 

(e)  Paste  of  Mercurous  and  Zinc  Sulphates. — Two  or  three 
parts  by  weight  of  mercurous  sulphate  are  added  to  one  part 
by  weight  of  mercury. 

If  the  sulphate  is  dry,  it  is  mixed  with  a  paste  consisting 
of  zinc  sulphate  crystals  and  a  concentrated  zinc  sulphate 
solution,  so  that  the  whole  constitutes  a  stiff  mass,  which  is 
permeated  throughout  by  zinc  sulphate  crystals  and  globules 
of  mercury.  If  the  mercurous  sulphate,  however,  is  not 
dry,  only  zinc  sulphate  crystals  are  to  be  added;  care  must 
be  taken,  however,  that  the  zinc  sulphate  crystals  are  in 
excess  and  are  not  dissolved  after  long  standing.  The  mer- 
cury must  in  this  case  also  permeate  the  paste  in  little  globules. 
It  is  advantageous  to  crush  the  zinc  sulphate  crystals  before 
using,  since  the  paste  can  be  beter  manipulated. 

Temperature  Coefficient. — The  temperature  coefficient  of 
the  Carhart-Clark  cell  is  one-half  of  that  of  the  Clark  cell. 
The  equation  connecting  the  E.M.F.  and  the  temperature 
for  the  Carhart-Clark  cell  is 

Et  =  1.440|  1-0.000387(£- 15)  +  0.0000005  (Z-15)2j. 
For  ordinary  room  temperatures  this  formula  may  be  simpli- 
fied thus: 

#f  =  1.440- 0.00056^-15). 


186 


ELECTRICAL  MEASUREMENTS. 


Weston  Standard  Cell. — Another  form  of  standard  cell 
(Fig.   80)     frequently    employed    in    the    physico-chemical 


FIG.  80. 

laboratory  is  that  invented  by  Edward  Weston.     The  cell  is 
constructed  upon  the  scheme: 

-  iCd|CdS04|Hg2S04|Hg|+. 

The  H  form  of  cell  has  been  chosen  as  best. 

Into  the  bottom  of  each  limb  is  sealed  a  platinum  wire. 
In  one  limb  is  an  amalgam  of  cadmium,  while  in  the  other 
limb  is  mercury  and  a  paste  of  mercurous  sulphate  mixed 
with  a  solution  of  cadmium  sulphate.  The  two  limbs  are 
connected  through  a  solution  of  cadmium  sulphate.  The 
E.M.F.  of  the  cell  is  1.019  volts,  and  the  temperature  coeffi- 
cient is  0.01  per  cent,  per  degree  centigrade. 

Helmholtz  One-volt  Cell. — A  cell  of  exactly  one  volt 
electromotive  force  is  very  ueeful  for  many  purposes.  The 
cell  shown  in  Fig.  81  was  devised  by  Helmholtz  in  1882. 


ELECTROMOTIVE  FORCE.  187 

The  electrodes  consist  of  amalgamated  zinc  and  mercury, 
the  mercury  being  covered  with  mercurous  chloride  and  a 
solution  of  zinc  chloride  (sp.  gr.  1.409). 

Since  zinc  chloride  is  usually  basic,  enough  hydrochloric 
acid  should  be  added  to  the  concentrated  aqueous  solution 
to  just  dissolve  the  white  residue.  Some  granulated  zinc 
should  also  be  added  to  the  zinc  chloride  solution  in  order  to 


CALOMEL  f 


FIG.  81. 

remove  any  cadmium  which  may  be  present.    When  the 
cell  is  assembled  it  will  give  an  E.M.F.  of  1  volt  ±0.01.     The 
temperature  coefficient  is  so  small  as  to  be  negligible. 
The  scheme  of  the  cell  is 

-  |Zn|ZnCl2|Hg2Cl2|Hg|+. 

Lippmann  Electrometer. — This  instrument  is  best  suited 
to  physico-chemical  purposes,  since  it  is  small  and  very 
slightly  affected  by  external  disturbances.  It  is  based  upon 
the  principle  that  the  curface  tension  of  mercury  in  contact 
with  dilute  sulphuric  acid  changes  when  there  is  a  change  in 
potential  between  the  points  of  contact.  One  surface  of 
contact  is  large  while  the  other  is  very  small,  since  when 
there  is  a  difference  of  potential  between  there  surfaces  it 
distributes  itself  in  the  ratio  of  the  surfaces  and  the  smaller 


1S8 


ELECTRICAL  MEASUREMENTS. 


electrode  is  thus  affected  almost  exclusively;  In  the  elec- 
trometer devised  by  Lippmann  the  small  electrode  is  caused 
to  assume  a  definite  position  under  the  action  of  the  molec- 
ular force.  When  a  difference  of  potential  is  introduced,  the 
resulting  movement  take,3  place  almoct  entirely  at  the  smaller 
surface,  thus  making  it  possible  to  measure  the  potential 
difference. 

A   very   convenient   form   of   electrometer   is   shown   in 
Fig.  82.     The  glass  apparatus  consists  of  a  small  flask,  b, 


FIG.  82. 

into  the  neck  of  which  is  fastened  a  small  capillary  tube,  c, 
which  terminates  in  a  larger  tube,  d.  This  is  attached  to  a 
thin  piece  of  wood,  which  is  fastened  to  a  heavy  base-board 
at  one  end  by  means  of  a  spring-hinge.  The  other  end  of  the 
strip  is  provided  with  an  adjusting-screw,  /,  by  means  of  which 
the  capillary  can  be  inclined  at  any  desired  angle  to  the 
base-board.  Beneath  the  capillary  c  there  is  placed  a  milli- 
metre scale  by  means  of  which  the  position  of  the  end  of 
the  mercury  column  may  be  accurately  noted. 

The  electrometer  is  made  ready  for  use  by  first  placing 
mercury  in  d  and  b  and  then  pouring  dilute  sulphuric  acid 
(1  :  6  by  volume)  into  b.  Connection  with  the  mercury  is 
made  by  means  of  two  platinum  wires,  the  wire  in  6  being 


ELECTROMOTIVE  FORCE. 


189 


protected  from  contact  with  the  acid  by  means  of  a  glass 
tube  fused  over  it.  These  wires  are  fastened  to  two  screw 
terminals.  The  binding-screws  are  connected  by  a  wire, 
and  a  drop  of  mercury  is  caused  to  pass  from  d  to  6.  By 


FIG.  83 

inclining  the  apparatus  and  manipulating  the  screw  /  the 
mercury  thread  can  be  brought  near  the  end  of  the  capillary. 
The  greater  the  inclination  the  more  rapidly  can  the  elec- 


190  ELECTRICAL  MEASUREMENTS. 

trometer  be  adjusted,  though  the  instrument  becomes  less 
sensitive  with  increase  in  the  angle  of  inclination.  By  ad- 
justing the  amount  of  mercury  in  d  the  sensitiveness  can 
be  controlled.  A  deflection  of  five  scale  divisions  for  0.01 
volt  is  very  convenient. 

A  more  sensitive  form  of  Lippmann  electrometer  is  shown 
in  Fig.  83.  With  this  instrument  five  scale  divisions  corre- 
spond to  0.001  volt.  The  increased  sensitiveness  is  due  to 
the  capillary  being  vertical.  The  position  of  the  mercury 
thread  is  read  by  means  of  a  small  microscope  magnifying 
about  30  diameters  and  provided  with  a  scale  in  the  eyepiece. 

The  mercury  column  is  illuminated  either  by  a  small 
electric  incandescent  lamp  or  by  a  concave  mirror  such  as  is 
used  on  microscopes. 

Since  it  is  necessary  to  keep  the  mercury  in  the  two  arms 
of  the  electrometer  in  electrical  connection  except  at  the 
instant  of  making  a  measurement,  a  key  devised  by  Ostwald 
is  extremely  useful.  This  is  shown  in  Fig.  84.  It  consists 


FIG.  84. 

of  a  strip  of  brass,  d,  connected  at  one  end  with  the  binding- 
screw  b  and  at  the  middle  with  the  screw  c.  Upon  pressing 
the  strip  downward  connection  is  established  between  b  and 
a,  while  connection  with  c  is  broken.  The  terminals  b  and 
c  are  kept  permanently  in  connection  with  the  terminals  of 
the  electrometer,  while  a  is  connected  with  the  potential  to 
be  measured. 

Use  of  the  Capillary  Electrometer.  —  When  using  the  elec- 
trometer, special  precautions  must  be  taken  to  insure  it 


ELECTROMOTIVE  FORCE. 


191 


against  polarization.  This  is  done  by  causing  the  current 
to  flow  through  it  from  the  large  electrode  to  the  capillary. 
The  proper  order  of  connections  is  shown  in  Fig.  85. 


FIG.  85. 


To  obtain  satisfactory  results  the  electrometer  must  be 
clean  and  the  mercury  used  must  also  be  free  from  im- 
purities. 

The  cleaning  of  the  electrometer  is  best  effected  by  means 


FIG.  86. 

of  hot  chromic   acid.      After    the  tube    has    been  in   the 
acid  for  sufficient  time  it  is  rinsed  with  water  and  theo 


192 


ELECTRICAL  MEASUREMENTS. 


washed  in  dilute  sodium  hydroxide  solution,  after  which  it 
is  thoroughly  washed  with  distilled  water  and  dried  by 
aspirating  hot  dry  air  through  it.  In  order  to  prevent  dust 
particles  from  being  carried  into  the  electrometer  the  air 
should  be  filtered  through  a  tube  containing  cotton-wool. 

It  is  well  when  using  the  electrometer  to  attach  a  small 
tube  containing  some  cotton- wool  as  shown  in  Fig.  86. 

If  the  electrometer  has  not  been  in  use  for  some  time,  it 
is  advisable  to  alternately  apply  pressure  and  suction  at  A 
before  attempting  any  measurements.  When  not  in  use 
the  mercury  in  the  two  arms  must  be  kept  in  electrical 
connection  through  the  key. 

The  Measurement  of  Electromotive  Force. — Of  the  many 
different  methods  which  have  been  devised  for  the  measure- 
ment of  E.M.F.,  the  Poggendorff  compensation  method  is  best 
adapted  to  the  requirements  of  the  physical-chemist.  In 
this  method  the  E.M.F.  to  be  measured  is  opposed  to  a  varia- 
ble E.M.F.,  the  latter  being  altered  until  the  one  cancels  the 
other.  The  general  scheme  of  the  method  is  shown  in  Fig.  87. 


FIG.  87. 

A  constant  element,  E,  having  a  greater  E.M.F.  than  that  to  be 
measured,  is  closed  through  the  resistance  ab.    The  element  n 


ELECTROMOTIVE  FORCE. 


193 


of  which  the  E.M.F.  is  sought  is  connected  through  the  gal- 
vanometer or  electrometer  G  with  a  and  the  sliding  contact  c. 
The  contact  c  is  moved  along  ab  until  the  instrument  G  indi- 
cates zero.  Call  this  position  of  c,  plf  Now  for  TC  we  sub- 
stitute a  standard  cell  (Carhart-Clark  or  Weston  element)  S, 
and  again  move  c  along  the  wire  until  a  balance  is  obtained. 
Denote  this  position  by  p2.  Then  we  have  the  proportion: 


or 


E.M.F.  of  TT:  E.M.F.  of  S=aPl 
E.M.F.  of 


E.M.F.  of  ?r  = 


ap2 


It  is  obvious  that  there  will  always  be  some  point  between 
a  and  c  where  the  potentials  of  E  and  TL  will  balance  provided 
the  potential  of  E  is  greater  than  that  of  TT. 

The  details  of  the  connections  for  an  electromotive  force 
measurement  are  given  in  Fig.  88.  The  accumulator  A 


FIG  88. 


is  connected  with  the  terminals  of  the  bridge  wire  ab,  a 
switch,  K,  being  included  in  the  circuit.  The  terminals  of 
the  wire  a&7  are  also  connected  with  the  electrometer  and 


194 


ELECTRICAL    MEASUREMENTS. 


the  cell  to  be  measured  as  shown  in  the  sketch.  The  two- 
way  switch,  R,  is  inserted  between  the  electrometer  and  the 
sliding  contact  C,  so  that  either  the  cell  to  be  measured  or 
the  standard  element  can  be  balanced  against  the  constant 
potential  difference  ab,  without  disconnecting  any  wires. 
A  very  convenient  form  of  two-way  switch  can  be  made 
by  boring  three  holes  part  way  through  a  piece  of  soft  pine, 
as  shown  in  Fig.  89,  filling  these  holes  with  mercury  and 
establishing  connection  by  means  of  a  bent  piece  of  heavy 
copper  wire. 

When  the  connections  have  been  made  as  shown  above 


FIG.  89. 


the  process  of  measuring  the  electromotive  force  is  extremely 
simple. 

The  key  K  is  closed,  the  two-way  switch  R  is  so  turned 
as  to  include  the  unknown  E.M.F.  in  the  circuit  and  the 
sliding  contact  C  is  moved  near  the  middle  of  the  bridge. 
The  electrometer  key,  S,  is  depressed  and  the  movement 
of  the  mercury  is  noticed.  If  it  moves  up,  the  contact 
C  is  moved  until  a  point  is  reached  where  the  mercury 
moves  in  the  opposite  direction  on  depressing  S.  The 
contact  C  is  now  moved  until  a  point  is  found  where 
the  mercury  just  begins  to  move  up  again.  The  point  of 
balance  lies  between  these  last  two  positions  of  C.  The 
exact  point  of  balance  may  be  determined  by  noting  the 


ELECTROMOTIVE  FORCE.  195 

number  of  scale  divisions  in  the  eye-piece  of  the  electrometer 
microscope  through  which  the  meniscus  is  displaced  and  then 
calculating  the  proportion  the  position  for  zero  displacement. 
For  example,  suppose  the  meniscus  moves  upward  over  7 
divisions  of  the  scale  for  a  bridge  reading  of  56.8  while  for 
a  bridge  reading  of  57.1  the  meniscus  is  displaced  downward 
through  4  divisions.  A  difference  of  0.3  cm.  on  the  bridge 
corresponds  to  a  displacement  of  11  scale  divisions,  hence 
from  the  proportion  0.3: 11  =  x:  4,  we  find  that  the  exact 
point  of  balance  is  0.1  cm.  below  57.1  or  the  correct  reading 
is  57.0.  After  having  made  several  measurements  of  the 
point  of  balance  for  the  E.M.F.,  the  two-way  switch  is 
turned  so  as  to  throw  in  the  standard  element  and  by  an 
exactly  similar  procedure  the  new  point  of  balance  is  deter- 
mined. 

By  means  of  the  formula  given  above  the  unknown  E.M.F. 
may  then  be  calculated.  Some  difficulty  may  be  experienced 
in  getting  satisfactory  response  of  the  mercury  meniscus 
as  the  point  of  balance  is  approached.  When  the  balance 
has  nearly  been  obtained,  the  key  S  should  be  depressed  for 
several  seconds  and  then  suddenly  released.  If  there  is  no 
movement  of  the  meniscus  the  point  of  balance  has  been  found. 

Potential  Differences. — In  all  galvanic  e!ements  the  total 
difference  of  potential  is  the  algebraic  sum  of  the  potential 
differences  at  the  points  of  contact  of  the  various  substances 
composing  the  galvanic  system. 

In  the  system 

-Zn|ZnS04|CuS04|Cu+ 

the  sources  of  potential  are  (a)  between  zinc  and  zinc  sul- 
phate (6)  between  copper  and  copper  sulphate;  (c)  between 
zinc  sulphate  and  copper  sulphate;  and  (d)  between  zinc  and 
copper.  Of  there  four  sources  of  potential  the  most  important 


196  ELECTRICAL   MEASUREMENTS. 

are  the  differences  existing  between  the  metals  and  the  solu- 
tions of  their  respective  sulphates.  Second  in  magnitude  is 
the  potential  difference  between  the  two  solutions,  while  of 
trivial  importance  is  the  potential  between  the  two  metals. 

The  potential  differences  existing  between  a  metal  and  a 
solution  depend  not  only  on  the  nature  of  the  metal,  but  also 
upon  the  concentration  of  the  metal  ions  in  the  solution. 
The  condition  of  the  surface  of  the  metal  has  often  a  marked 
influence  upon  the  electromotive  force.  It  is  advisable 
when  possible  to  use  the  metal  in  the  form  of  an  amalgam,  thus 
insuring  a  well-defined  surface.  The  electromotive  force  of 
an  amalgam  is  nearly  the  same  as  that  of  the  pure  metal,  but 
does  undergo  some  change  with  the  strength,  so  that  the 
concentration  must  always  be  ascertained. 

The  most  convenient  means  of  preparing  an  amalgamated 
electrode  is  to  pass  an  electric  current  through  a  solution  of 
the  salt  of  the  metal,  using  mercury  as  the  cathode  and  a 
platinum  wire  for  the  anode.  By  including  a  silver  volt- 
ameter in  the  circuit  the  exact  quantity  of  metal  deposited 
can  be  calculated. 

The  potential  differences  existing  between  solutions  is 
wholly  dependent,  as  Nernst  has  shown,  upon  the  relative 
velocities  of  the  ions.  In  the  system  cited  above,  copper  and 
zinc  having  nearly  equal  verities  of  migration,  the  potential 
difference  is  practically  negligible.  In  the  investigation'  of 
potential  differences,  the  electrolyte  is  poured  into  a  tube 
through  the  stopper  of  which  passes  the  electrode;  to  the 
side  of  the  tube  is  sealed  a  r  iphon-tube  which  serves  to  con- 
nect it  through  an  intermediate  vessel  (beaker)  with  a  similar 
tube  also  provided  with  an  electrode.  This  apparatus  is 
shown  in  Fig.  90, 

Normal   Electrodes. — In  order  to  measure  the  difference 


ELECTROMOTIVE  FORCE. 


197 


of  potential  between  an  electrode  and  an  electrolyte  it  is 
necessary  to  employ  another  electrode  and  generally  another 
electrolyte.  For  this  reason  it  is  advisable  to  use  the  same 
electrode  and  same  electrolyte  in  all  measurements  of  differ- 
ences of  potential  between  metals  and  their  electrolytes. 
Such  a  standard  electrode  is  known  as  a  normal  electrode. 

The  most  satisfactory  of  several  proposed  normal  elec- 
trodes is  that  devised  by  Ostwald  and  shown  in  Fig.  91. 


FIG.  90. 


Pure  mercury  is  poured  on  the  bottom  of  the  vessel,  and  upon 
this  there  is  placed  a  layer  of  mercurous  chloride  and  then  a 
normal  solution  of  potassium  chloride.  By  means  of  the 
platinum  wire  which  is  sealed  into  the  bottom  of  the  vessel 
connection  is  established  with  the  mercury,  while  by  means 
of  the  siphon-tube  containing  potassium  chloride  solution 
the  normal  electrode  can  be  put  in  communication  with  the 
electrolyte  under  investigation.  The  difference  of  potential 


198 


ELECTRICAL  MEASUREMENTS. 


between  the  mercury  and  potassium  chloride  is  0.56  volt  at 
room  temperature,  or  more  exactly 


-7T«KC1  =  +0.56  +0.0006(7  -  18°). 

It  is  to  be  noted  that  the  mercury  is  positive  to  the  potassium 


FIG.  91. 


chloride.  The  following  example  will  make  clear  the  use  of 
the  normal  electrode :  It  is  desired  to  determine  the  potential 
difference  between  zinc  and  a  normal  solution  of  zinc  sulphate. 
The  system  then  takes  the  form 

Zn-nZnSO,  -nKCl,HgCl-Hg. 

Against  the  normal  electrode  we  find  7r  =  1.08  volts,  the  cur- 
rent flowing  in  the  direction  of  the  arrow.  From  the  funda- 


ELECTROMOTIVE  FORCE.  199 

mental  theory  of  the  cell  we  know  the  total  E.M.F.  to  be 
given  by  the  equation 

RT  .       P    RT.       Pr 


where  P  and  p  are  the  solution  tension  and  osmotic  pressure 
of  the  zinc  ions  respectively,  and  where  P'  and  p'  are  the 
corresponding  values  for  mercury.  We  then  have 


or 


=       log  £+0.56, 


?T-  log£~  =(1-08-0.56)  =  +0.52  volt. 

2e0        c  p 


In  other  words,  zinc  is  positive  against  a  normal  solution  of 
its  sulphate  and  gives  an  electromotive  force  of  0.52  volt. 
It  is  to  be  borne  in  mind  that  the  sign  always  refers  to  the 
potential  of  the  electrolyte  against  the  electrode. 

Preparing  the  Electrodes.  —  In  the  preparation  of  «elec- 
trodes  for  E.M.F.  measurements  the  pure  metal,  either  in 
the  form  of  rods  or  sheets,  is  cut  to  convenient  size.  For 
rods  a  convenient  length  is  3  cm.,  while  for  sheets  it  is  usual 
to  employ  a  surface  of  1.5  cm.  Xl  cm.  To  either  one  or  the 
other  of  these  forms  a  small  copper  wire  is  soldered  and  then 
the  electrode  and  connecting  wire  is  cemented  into  a  glass 
tube,  care  being  taken  that  the  cement  or  sealing  wax  com- 
pletely covers  the  soldered  junction. 

These  glass  tubes  are  then  ready  for  mounting  in  the  cells 
shown  in  Fig.  90.  Before  using  the  electrodes,  however, 
they  should  be  rendered  as  uniform  as  possible. 

This  is  accomplished  in  the  case  of  zinc  and  cadmium 
electrodes  by  amalgamation  with  mercury.  The  electrodes 
are  first  dipped  in  dilute  sulphuric  acid  and  then  rubbed 
with  mercury  by  means  of  a  swab  of  wool  or  cotton. 


200  ELECTRICAL  MEASUREMENTS. 

Copper,  silver,  or  platinum  electrodes  are  rendered 
uniform  by  means  of  electrolysis.  The  electrode  is  made 
the  cathode  in  a  dilute  electrolytic  bath  of  a  salt  of  the 
metal  of  the  electrode  and  a  small  current  is  allowed  to 
flow  until  a  fine-grained,  adherent  deposit  of  the  metal  is 
obtained. 

The  current  density  for  this  deposition  should  not  exceed 
0.5  ampere  per  square  decimeter  of  cathode  surface. 

It  is  desirable  to  prepare  electrodes  in  duplicate  and 
before  using  them  for  an  E.M.F.  determination  to  ascer- 
tain whether  an  E.M.F.  is  set  up  when  they  are  immersed 
in  the  same  solution.  The  testing  of  the  electrodes  is  carried 
out  as  follows :  Set  up  a  cell  as  shown  in  Fig.  90  and  let  us 
suppose  that  we  are  employing  copper  electrodes.  Fill 
each  arm  of  the  cell  and  the  intermediate  vessel  with  a  deci- 
normal  solution  of  copper  sulphate.  The  cell  is  now  put 
in  the  place  of  Y  in  Fig.  88  and  is  connected  in  series  with 
the  standard  cell  X.  First  the  point  of  balance  is  deter- 
mined with  X  alone  and  then  for  X  and  Y  together.  Ob- 
viously if  the  copper  electrodes  are  similar  and  uniform  the 
point  of  balance  should  be  the  same  in  both  cases.  If, 
on  the  other  hand,  there  is  a  difference  of  more  than  0.001 
volt,  the  copper  electrodes  should  be  replaced  in  the  elec- 
troyltic  bath  and  given  an  additional  deposit  of  copper. 
When  there  is  no  appreciable  difference  in  potential  between 
the  two  electrodes  they  may  be  used  for  E.M.F.  determi- 
nations. 

Measurement  of  the  Potential  Difference  between  a  Metal 
and  a  Solution  of  a  Salt  of  the  Metal. — Having  prepared  a 
uniform  electrode  of  the  metal  M  it  is  fixed  in  one  of  the 
electrode  vessels  and  this  is  filled  with  a  deci-normal  solution 
of  MS04.  This  is  now  connected  with  a  normal  calomel 
electrode  through  an  intermediate  vessel  by  means  of  a  2 


ELECTROMOTIVE  FORCE.  201 

or  3  normal  solution  of  KCL     We  then  have  the  following 
system : 


M 


MS04  2nKCl 


HgCl 
n-KCl 


Hg. 


We  first  determine  the  point  of  balance  with  the  standard 
cell,  and  then  replace  it  by  the  above  system.  If  the  mer- 
cury meniscus  in  the  electrometer  moves  constantly  in  one 
direction,  no  matter  where  the  sliding  contact  is  placed  on 
the  bridge  wire,  it  shows  that  the  composite  cell  has  been 
connected  in  reverse  order  and  we  must  interchange  the 
connecting  wires. 

When  this  has  been  done  no  difficulty  should  be  experi- 
enced in  getting  a  satisfactory  balance  on  the  bridge  wire. 

In  this  manner  we  determine  not  only  the  quantities 
necessary  for  the  calculation  of  the  E.M.F.  of  the  system; 
but  also  ascertain  the  positive  pole  of  the  combination. 

Should  the  point  of  balance  fall  near  the  end  of  the  bridge 
wire,  it  is  desirable,  in  order  to  secure  greater  accuracy 
to  join  the  experimental  cell  and  the  standard  cell  in  series, 
thus  determining  a  point  of  balance  corresponding  to  the 
combined  E.M.F.  of  both  cells.  This  procedure  will  be 
found  necessary  in  all  cases  where  the  E.M.F.  of  the  cell  is 
small. 

The  E.M.F.  of  the  combination  cell  is  then  given  by  the 
equation, 

E.M.F.  of  (X+S)    a 


E.M.F  of  AS      ~b 


where  X  is  the  unknown  E.M.F.,  S  the  E.M.F.  of  the  standard 
cell  and  a  and  b  are  the  corresponding  bridge  readings. 

Knowing  the  potential  of  the  normal  calomel  electrode, 
the  potential  difference  between  the  metal  and  the  solution 
can  be  calculated  as  shown  on  p.  120. 


202  ELECTRICAL  MEASUREMENTS. 

In  an  exactly  similar  manner  the  potential  difference 
between  a  metal  M'  and  the  solution  of  one  of  its  salts  may 
be  obtained,  and  from  this  result  the  E.M.F.  of  the  system 


may  be  calculated.  This  result  can,  of  course,  be  checked 
by  a  direct  measurement  of  the  E.M.F.  of  the  latter  com- 
bination. 

Concentration  and  Potential  Difference.  —  It  is  shown  in 
text-books  of  electro-chemistry  that  the  potential  difference 
between  a  metal  and  a  solution  is  a  function  of  the  con- 
centration of  the  cations  in  solution. 

If  we  have  the  combination 

Ag  |  dil.  AgN03  |  cone.  AgN03  |  Ag 
the  equation  for  the  potential  difference  of  the  system  is 

TT  =  RT  log,  --RT  log£—. 
p  p 


Since  P=Pf  we  have 


And  since  osmotic  pressure  is  directly  proportional  to  the 
centration  we  have 

x=RTlo&-,. 
c 

Assuming  room  temperature  to  be  17°  C.,  the  above  equa- 
tion reduces  to 

*r-0.0581oglop. 


ELECTROMOTIVE  FORCE.  203 

This   equation  holds   for  a  completely  dissociated  electro- 
lyte. 

Where  dissociation  is  not  complete,  as  is  usually  the  case, 
the  percentage  dissociation  of  the  solutions  must  be  con- 
sidered. The  equation  then  becomes 

TT  =  0.058  loio-. 


Concentration  Cells  Involving  Ionic  Migration.  —  In  cells 
of  this  type  the  E.M.F.  is  not  equal  to  the  sum  of  the  two 
electrode  potentials  as  measured  against  a  normal  calomel 
electrode,  but  involves  the  ionic  velocities  of  the  cation 
and  anion  of  the  electrolyte.  If  u  is  the  ionic  velocity  of 
the  cation  and  v  the  velocity  of  the  anion,  and  n  is  the 
valence  of  the  cation,  then  the  E.M.F.  of  a  cell,  where  the 
positive  and  negative  ions  have  markedly  different  speeds, 
is  given  by  the  equation, 

v       0.058  .        c 


71  = 


-  iQ-;. 

n  c' 


Solution  Pressure.  —  From  the  potential  difference  between 
a  metal  and  its  salt  solution  we  can  calculate  the  solution 
pressure  of  the  metal  in  atmospheres.  From  the  well  known 
equation, 

RT.       P 

7T  =  --  log£  - 

ne      D  p 
we  get 

,        „    Tine 
logs  P— 


or  if  the  room  temperature  be  17°  C.  this  becomes 

nne 


204  ELECTRICAL  MEASUREMENTS. 

By  using  normal  solutions  and  knowing  the  percentage 
dissociation  a,  p  becomes  22  a  atmospheres. 

Solubility  from   E.M.F.  Measurements. — The  well-known 

r 
formula  71  =  0.058  Iog10  ~n  having  been  verified  experiment- 

G 

ally,  we  may  use  it  with  certainty  to  determine  the  solubility 
of  difficultly  soluble  salts.     This  method  is  very  useful  in 
cases  where  the  solubility  is  so  small  as  to  render  a  deter- 
mination by  chemical  means  entirely  untrustworthy. 
Suppose  that  we  have  the  system, 

Ag  |  0.001 -nAgNOa  |  n-KN03  |  n-KN03  |  Agl  |  Ag. 

The  electromotive  force  of  this  combination  is  measured 
with  due  precautions  and  is  found  to  be  0.22  volt.  In  a 
0.001  —  n  silver  nitrate  solution,  dissociation  is  so  nearly 
complete  that  we  will  commit  no  serious  error  in  assuming 
the  concentration  of  the  silver  ions  to  be  0.001.  From  the 
formula  we  then  have 

Iog10c'  =  0.058  log™  c-0.22, 
or  Iog10  c' = 0.058  logio  0.001  -  0.22. 

Solving,  we  find  that  c'  =  1.6  X 10  -  8  or  1000  cc.  of  a  satu- 
rated solution  of  Agl  contains  1.6XlO~8  gram-molecules  of 
Agl  or  0.0000035  gr.  Agl.  The  corresponding  value  obtained 
by  the  conductivity  method  is  1.5XlO~8. 

Gas  Cells. — In  the  several  cells  which  have  been  described 
in  the  preceding  paragraphs,  soluble  reversible  electrodes 
have  been  employed,  the  solution  or  deposition  of  the  metal 
ions  being  the  chief  cause  of  the  resulting  electromotive 
force. 

If  the  soluble  electrodes  be  replaced  by  platinum  or  some 


ELECTROMOTIVE  FORCE.  205 

metal  of  the  platinum  group  we  have  a  means -of  measuring 
the  electromotive  force  of  combinations  in  which  metallic 
ions  are  not  involved.  If  the  electrode  be  surrounded  with 
a  gas  such  as  hydrogen,  and  partially  immersed  in  a  solution 
containing  hydrogen  ions,  it  will  behave  as  a  reversible 
hydrogen  electrode,  its  potential  being  a  function  of  the 
concentration  of  the  hydrogen  ions  in  the  solution  and  the 
gas-pressure  in  the  electrode  vessel.  These  cells,  in  which 
gases  are  the  active  agents  in  the  production  of  electro- 
motive force,. are  known  as  gas  cells.  The  theory  of  their 
action  is  in  no  way  different  from  that  of  the  cells  already 
discussed. 

Assuming  for  illustration  a  cell  made  up  as  follows: 

H2  |  0.1  -n  HC1 1  0.01  -n  HC1 1  H2, 

we  may  calculate  its  E.M.F.  by  means  of  the  equation  given 
in  the  paragraph  dealing  with  concentration  cells  involving 
ionic  migration,  viz.. 

v       0.058  _        c 
logio-. 


n  —       .  jA^ii*"    ,, 

u  +  v        n  c' 

It  is  necessary  to  take  the  ionic  velocities  into  account 
here  since  the  hydrogen  ion  has  a  velocity  so  much  in  excess 
of  the  other  ions. 

The  electrodes  for  this  type  of  cell  are  best  made  by  de- 
positing platinum  on  a  glass  tube  in  a  thin  film,  for  if  foil 
be  used  much  time  must  be  given  the  system  before  it  comes 
to  equilibrium,  and  then  the  results  are  likely  to  be  unsatis- 
factory. 

The  method  of  preparing  an  electrode  for  a  gas  cell  is 
very  simple,  and  with  a  little  practice  the  student  may  become 
proficient  in  platinizing  the  tubes.  A  piece  of  glass  tubing 


206 


ELECTRICAL  MEASUREMENTS. 


of  suitable  diameter  and  length,  is  drawn  out  as  shown  in 
Fig.  92a,  the  neck  N  being  sealed,  while  the  other  end  A 
is  left  open. 

With  a  camel's-hair  brush  the  tube  is  painted  with  a 
platinum  solution  specially  prepared  for  the  purpose,  the 
solution  being  applied  over  the  entire  surface  down  to  the 


FiG.92a. 


FIG.  926. 


contraction  at  A.  The  tube  is  now  held  over  the  Bunsen 
flame  and  dried  in  the  upward  current  of  heated  air. 

Care  should  be  taken  at  this  point  to  dry  slowly  and 
uniformly  thus  avoiding  blisters.  After  a  few  moments 
the  film  begins  to  darken  and  finally  becomes  totally  black. 

The  heating  is  then  continued  until  the  lustre  of  metallic 
platinum  appears,  when  the  tube  is  subjected  to  a  higher 
temperature,  and  finally,  when  the  last  traces  of  organic 
matter  have  disappeared,  it  is  heated  to  redness  in  the  blow- 
pipe flame.  During  the  whole  of  the  heating  the  tube  must 


ELECTROMOTIVE  FORCE. 


207 


be  slowly  rotated  and  in  the  last  stage  it  must  not  be  heated 
strongly  enough  to  cause  the  tube  to  lose  its  shape. 

Should  the  deposit  prove  too  thin,  another  coat  of  the 
platinizing  solution  may  be  added  as  soon  as  the  tube  is 
cool.  After  a  satisfactory  coating  has  been  obtained  the 
tube  is  sealed  off  at  A  and  is  fastened  into  the  glass  tube 
T,  Fig.  926,  by  means  of  sealing-wax.  By  means  of  mercury 


FIG.  93. 

and  a  copper  wire  connection  with  the  electrode  is  estab- 
lished, as  shown  in  the  illustration.  When  not  in  use  the 
electrode  should  be  kept  in  distilled  water. 

The  special  form  of  electrode  vessel  required  for  experi- 
ments with  gas  cells  is  shown  in  Fig.  93. 

The  wide  glass  tube  A  serves  to  contain  the  gas  and  the 
electrolyte.  To  it  are  sealed  three  tubes,  B,  C,  and  D,  which 
communicate  with  the  gas  generator,  the  other  half  of  the 
cell  and  the  mercury  seal  F,  respectively. 


208  ELECTRICAL  MEASUREMENTS. 

The  stopper  carries  the  electrode  and  connecting  wire. 
In  making  a  measurement  of  electromotive  force  of  the 
system 

H2|0.1-nHCl    0.01-nHCl|H2 

we  would  proceed  in  the  following  manner:  The  two  elec- 
trode vessels  are  filled  with  0.1  —  n  HC1,  the  stop-cocks  C 
being  opened  and  the  exit  tubes  F  being  closed.  Carefully 
purified  hydrogen  is  then  passed  through  the  electrode 
vessels  until  the  acid  has  been  forced  out  to  the  level  of 
the  tubes  C,  when  the  stop-cocks  are  closed  and  the  gas 
is  allowed  to  bubble  slowly  through  the  mercury-seal  F. 
This  is  continued  for  nearly  three-quarters  of  an  hour  and 
then  the  gas  is  shut  off.  It  will  be  found  that  after  a  short 
time  the  electrodes  will  absorb  enough  hydrogen  to  create 
a  partial  vacuum  in  the  vessel  A  and  care  must  be  taken  to 
prevent  the  entrance  of  air  through  the  mercury-seal  F. 
Should  it  be  necessary,  more  hydrogen  is  passed  until  the 
electrodes  become  thoroughly,  saturated  with  the  gas.  The 
ends  of  the  tubes  C  are  now  dipped  in  0.1  —  n  HC1,  the  stop- 
cocks are  opened  and  the  uniformity  of  the  electrodes  is 
tested.  If  no  electromotive  force  is.  set  up  between  them, 
their  uniformity  is  established,  and  we  may  then  enter  upon 
the  measurement  of  the  E.M.F.  of  the  system  under  investi- 
gation. One  electrode  vessel  is  filled  with  0.01—  n  HC1 
and  hydrogen  is  passed  in  as  before. 

When  absorption  is  complete  the  two  halves  of  the  cell 
are  connected  through  an  intermediate  vessel  containing 
O.lXnHCl  and  the  E.M.F.  is  measured.  Owing  to  the 
small  value  of  the  E.M.F.  measured,  the  cell  must  be  joined 
in  series  with  the  standard  cell.  Several  measurements 
should  be  made  at  intervals  of  twenty  minutes,  hydrogen 
being  passed  through  the  cell  in  the  meantime. 


CHAPTER  XII. 

MEASUREMENT  OF  CURRENT  AND  TRANSPORT  NUMBERS. 

OF  the  various  methods  for  measuring  the  electric  cur- 
rent, that  based  upon  electrolysis  is  best  adapted  to  the  re- 
quirements of  the  physical-chemist. 

Faraday  's  law  may  be  summarized  by  the  equation 

m  =Kit, 

where  m  is  the  mass  of  metal  deposited  by  current  i  in  time 
t,  and  where  K  is  a  proportionality  factor  known  as  the  elec- 
trochemical equivalent. 

It  is  at  once  apparent  that  if  the  mass  of  deposited  metal, 
the  electrochemical  equivalent  for  that  metal,  and  the  time 
during  which  electrolysis  is  taking  place  be  known,  then  the 
strength  of  current  is  determined  by  the  equation 

m 


The  electrolytic  cell  by  which  current  strength  is  deter- 
mined is  known  as  a  voltameter. 

Several  different  voltameters  adapted  to  such  conditions 
as  are  likely  to  be  met  with  in  the  physico-chemical  laboratory 
will  be  described. 

The  Silver  Voltameter  (Fig.  94).  —  For  currents  as  large 
as  one  ampere  the  cathode  should  consist  of  a  platinum  dish 
about  10  cm.  in  diameter  and  5  cm.  in  depth.  The  anode 
should  be  a  circular  plate  .of  pure  silver  2  mm.  thick  and 

209 


210 


ELECTRICAL  MEASUREMENTS. 


having  an  area  of  about  30  sq.  cm.  This  is  placed  in  a 
horizontal  position  near  the  surface  of  the  liquid  in  the 
platinum  dish,  the  supporting  wire  being  also  of  platinum. 

The  anode  should  be  covered  with  a  wrapping  of  fine 
muslin  or  filter-paper  to  prevent  any  disintegrated  particles 
of  silver,  silver  oxide,  or  carbon  from  falling  into  the  dish. 

The  platinum  dish  rests  upon  an  insulated  copper  sup- 

4- 


FIG.  94. 

port  which  serves  to  connect  it  with  the  negative  terminal  of 
the  source  of  current,  while  the  anode  wire  is  directly  con- 
nected with  the  positive  terminal.  The  electrolytic  bath 
should  consist  of  a  neutral  solution  of  silver  nitrate  con- 
taining 15  parts  of  pure  silver  nitrate  to  85  parts  of  pure 
redistilled  water.  The  method  of  carrying  out  a  measure- 
ment is  as  follows:  The  platinum  dish  is  washed  with  nitric 
acid  and  then  with  distilled  water,  and  then  heated  to  red- 
ness over  a  Bunsen  burner,  after  which  it  is  allowed  to  cool  in 
a  desiccator  and  then  carefully  weighed.  The  copper  sup- 
port is  cleaned,  and  the  dish  is  placed  upon  it.  The  dish  is 
then  nearly  filled  with  the  silver  nitrate  solution,  and  the 
anode  immersed  so  that  the  silver  plate  is  completely  cov- 
ered with  the  solution.  The  anode  is  then  connected  with 
the  positive  terminal,  and  the  circuit  closed  by  means  of  a 


MEASUREMENT  OF  CURRENT.  211 

key.  The  time  is  accurately  noted  at  which  the  circuit  is 
closed.  The  current  is  then  allowed  to  pass  for  at  least  half 
an  hour;  the  time  being  taken  again  when  the  current  is 
broken.  It  is  evident  that  the  clock  or  watch  employed 
must  be  a  reliable  time-keeper.  The  solution  is  now  poured 
out  of  the  dish,  the  silver  deposit  washed  several  times 
with  distilled  water,  and  .  the  dish  filled  with  distilled 
water  is  set  aside  for  six  hours.  The  dish  is  then  emptied 
and  again  washed  with  distilled  water,  the  washings  being 
collected  and  tested  for  silver  nitrate  with  hydrochloric  acid. 
If  no  cloudiness  appears,  the  dish  is  washed  with  absolute 
alcohol  and  dried  in  an  air-bath  at  150°  C.  It  is  then  cooled 
in  a  desiccator  and  weighed.  The  gain  in  weight  gives  the 
silver  deposited.  The  current  in  amperes  is  then  found  by 
substituting  in  the  equation 

.     m 


where  7£  =0.001118,  where  t  is  expressed  in  seconds,  and 
where  m  is  expressed  in  grams.  Instead  of  dividing  by  the 
time  of  deposit  in  seconds  and  by  0.00118,  the  time  may  be 
expressed  in  hours  and  fractions  thereof,  and  K  may  be  made 
equal  to  4.025. 

Copper  Voltameter.  —  When  large  currents  are  to  be 
measured  the  silver  voltameter  is  replaced  by  the  copper 
voltameter,  since  the  size  of  silver  plates  required  would 
make  the  former  too  expensive.  While  the  copper  voltame- 
ter is  by  no  means  as  accurate  an  instrument  as  the  silver 
voltameter,  owing  to  the  smaller  electrochemical  equivalent 
and  the  partial  oxidation  of  the  deposited  metal,  yet  it  has 
the  advantage  of  easier  manipulation  owing  to  the  firmly 
adherent  deposit  of  copper. 

For  large  currents  the  copper  plates  need  be  only 


212  ELECTRICAL  MEASUREMENTS. 

fifth  as  large  as  the  silver  plates  required  for  the  same  cur- 
rent. About  50  sq.  cm.  per  ampere  is  sufficient  for  good 
results  with  the  copper  voltameter.  The  copper  voltameter 
consists  of  two  plates  of  copper  suspended  in  a  copper  solu- 
tion contained  in  a  glass  vessel.  The  solution  to  be  employed 
is  the  following: 

Copper  sulphate 15  grams 

Sulphuric  acid 5      " 

Alcohol 5      '-', 

Water 100      '.5 

The  cathode  plate  before  use  should  be  carefully  smoothed 
at  the  edges,  the  corners  should  be  rounded  and  the  surface 
of  the  plate  should  be  polished  with  very  fine  sandpaper. 
After  this  treatment  the  plate  should  be  thoroughly  washed 
with  distilled  water  and  then  dried  on  clean  heavy  filter- 
paper.  The  plate  should  be  very  gently  heated  before  plac- 
ing in  the  desiccator  preparatory  to  weighing. 

The  process  of  determining  the  current  strength  is  exactly 
analogous  to  that  for  the  silver  voltameter.  The  electro- 
chemical equivalent  for  copper  is  0.0003294  if  the  time  be 
reckoned  in  seconds,  or  1.1858  if  in  hours. 

Transport  Numbers. — If  in  electrolysis  the  cations  and 
anions  migrate  with  equal  velocities,  the  change  in  con- 
centration around  the  electrodes  will  be  the  same.  Hittorf 
pointed  out  that  as  this  was  not  generally  the  case  the  ions 
must  move  with  different  speeds,  and  that  from  the  con- 
|centration  changes  at  the  electrodes  it  would  be  possible  to 
determine  the  relative  velocities  of  the  ions.  Since  the 
number  of  cations  discharged  at  the  cathode  is  equivalent 
to  the  number  discharged  at  the  anode,  and  since  the  veloci- 
ties of  migration  are  different  under  the  same  potential 
gradient,  it  follows  that  the  quantity  of  electricity  carried 
in  one  direction  by  the  cations  must  be  different  from  that 


TRANSPORT  NUMBERS.  213 

carried  by  the  anions  in  the  opposite  direction.  The  quan- 
tities of  electricity  so  carried  are  in  the  ratio  of  the  speeds 
of  migration  of  the  cation  and  anion  respectively.  The 
total  quantity  of  electricity  which  passes  through  the  solu- 
tion is  evidently  proportional  to  the  combined  velocities  of 
cation  and  anion,  from  which  it  follows  that  the  respective 
fractions  of  the  total  current  '  carried  by  the  cation  and 

anion  will  be  -    -  and  -       ,  where  u  and  v  denote  the  veloci- 

u  +  v 


ties  of  cation  and  anion. 

To  these  fractions  Hittorf  gave  the  name  transport  numbers. 
It  is  clear  then  that  to  determine  a  transport  number  all 
that  is  required  is  the  total  amount  of  current  passing  through 
the  solution  and  the  concentration  change  around  one  of 
the  electrodes. 

Many  forms  of  transport  vessel  have  been  devised,  but  for 
general  laboratory  use  a  modification  of  one  of  the  earliest 
types  is  very  satisfactory. 

In  Fig.  95  the  arrangement  of  the  apparatus  is  shown. 
The  two  vertical  limbs  A  and  B  are  connected  by  the  short 
horizontal  tube  C.  Each  tube  is  closed  at  the  top  by  rubber 
stoppers  carrying  the  glass  tubes  which  connect  with  the 
electrodes,  and  A  is  provided  at  the  bottom  with  a  glass 
stop-cock. 

The  electrodes  are  of  heavy  wire,  which  is  sealed  into  the 
glass  tubes  by  means  of  sealing-wax  or  a  cement  made  from 
litharge  and  glycerine.  The  electrodes  are  then  connected 
with  the  wires  in  the  glass  tubes  either  by  means  of  mercury 
or  they  are  soldered  to  the  wires  previous  to  sealing  them 
in  the  tubes. 

Care  should  be  taken  to  have  the  electrodes  thoroughly 
clean,  and  to  this  end  it  is  advisable  wherever  possible  to 
wash  them  with  acid  and  then  wash  with  distilled  water. 


214 


ELECTRICAL  MEASUREMENTS. 


To  illustrate  the  method  of  determining  a  transport  num- 
ber we  will  give  the  details  of  the  procedure  in  determining 
the  transport  numbers  of  the  silver  ion  and  the  N03  ion  in 
an  AgN03  solution.  It  is  only  necessary  to  employ  a  silver 


FIG.  95. 

anode,  since  we  shall  wish  to  know  only  the  concentration 
change  taking  place  around  the  anode.  The  cathode  may 
be  of  copper.  If  a  copper  cathode  be  employed,  the  short 
limb  B  of  the  transport  vessel  is  about  half  filled  with  a 
concentrated  solution  of  copper  nitrate  which  has  been 


TRANSPORT  NUMBERS. 


215 


acidified  with  HN03,  and  the  rest  of  the  vessel  is  filled  with 
a  solution  of  0.05-n  AgN03.  In  filling  the  limb  B  with 
the  AgN03  solution,  care  must  be  taken  not  to  disturb  the 
layer  of  concentrated  CuN03.  This  is  best  accomplished 
by  adding  the  AgN03  solution  from  a  pipette,  letting  the 
solution  flow  down  the  walls  of  B  in  a  slow  stream.  When 
the  vessel  is  filled  the  electrodes  are  inserted,  the  silver 
electrode  in  A  and  the  copper  electrode  in  B. 

Mfti/W ifi'hl'l'i 


The  transport  vessel  is  then  placed  in  the  circuit  as  shown 
in  Fig.  96. 

The  current  from  the  battery  B  flows  through  a  sliding 
resistance  R,  a  milliammeter  A,  a  silver  voltameter  V,  and 
then  through  the  transport  vessel  T.  The  current  is  broken 
by  means  of  the  switch  K.  A  current  of  from  10  to  20 
milliamperes  is  sent  through  the  apparatus,  the  approximate 
value  being  obtained  by  means  of  the  resistance  and  the 
milliammeter.  Care  should  be  taken  to  avoid  the  use  of 
too  strong  currents,  since  the  heating  effects  cause  convec- 
tion currents  in  the  transport  vessel  and  thus  vitiate  the 
results. 

The  silver  voltameter  is  to  be  prepared  as  described  at 


216  ELECTRICAL  MEASUREMENTS. 

the  beginning  of  this  chapter.  The  voltage  required  to  give 
the  desired  amount  of  current  will  be  dependent  upon  the 
dimensions  of  the  apparatus,  the  concentration  of  the  solu- 
tions, and  the  resistance  of  the  circuit.  As  a  rule,  it  will 
be  found  necessary  to  use  a  voltage  of  40  to  50  volts,  so  that 
where  it  is  possible,  the  use  of  the  electric  lighting  circuit 
is  to  be  recommended. 

Before  commencing  the  experiment  the  cathode  of  the 
silver  voltameter  is  weighed,  as  directed  above,  and  then  the 
current  is  allowed  to  flow  through  the  apparatus  for  about 
2  hours. 

The  cathode  of  the  voltameter  is  now  weighed  again  and 
the  total  current  which  has  passed  is  determined.  By  means 
of  the  stop-cock  D,  the  AgN03  solution  around  the  anode 
is  drawn  off  in  two  portions  into  two  previously  weighed 
flasks;  two-thirds  into  the  first  flask  and  the  remaining 
third  into  the  second. 

The  solutions  are  then  weighed  and  the  amount  of  silver 
in  each  is  determined  by  titration.  If  the  second  flask, 
which  contains  the  middle  layer  of  solution  in  the  transport 
vessel,  does  not  have  the  same  silver  content  as  the  original 
solution,  we  know  that  the  electrolysis  has  been  continued 
too  long  and  the  experiment  must  be  repeated.  If,  on  the 
other  hand,  the  titration  shows  the  second  flask  to  have 
identically  the  same  concentration  as  the  original  solution, 
we  may  proceed  to  the  calculation  of  the  transport  numbers. 

Let  us  suppose  that  before  electrolysis  the  solution  had 
the  composition, 

Water W  grams 

AgN03.. g 

We  then  determine  the  number  of  gram  equivalents  of 
silver  for  every  W  grams  of  water  as  follows : 


TRANSPORT  NUMBERS.  217 

AgN03  :  Ag  ::  179.97  : 107.93  ::  g  :  x. 

z/107. 93  =  number  of  gram  equivalents  of  Ag. 

After  electrolysis  the  solution  had  the  composition: 

Water W'  grams 

AgN03 g'       " 

Here  for  every  W  grams  of  water  we  have  2//107.93  gm. 
equivalents  of  Ag. 

Had  the  concentration  of  the  solution  remained  unchanged 

W'\x         X 

107  93 
W  grams  of  water  would  have  contained  -  -  gram 

equivalents  of  Ag.     The  increase  in  Ag  has  been,  therefore, 


y  'N  107.93  .     ,  ,  A 

1A-  no — F?T~    ~  Sm-  equivalents  of  Ag. 

107.9o 

The  weight  of  silver  deposited  in  the  voltameter  was  A 
grams  or  A/107.93  gm.  equivalents.  If  there  had  been  no 
migration  of  Ag  ions  there  should  have  been  an  increase 
of  A/107.93  gm.  equivalents.  The  actual  increase  was 
found  to  be 

x 

y  *  107.93 

107.93"       ~W~ 

and  hence  the  loss  due  to  migration  has  been 


107.93 


y  "107.93 


107.93  W 


gm.  equivalents, 


which  number  is  directly  proportional  to  the  velocity  of  the 


218 


ELECTRICAL  MEASUREMENTS. 


silver  ion.    The  fraction  of  the  current  carried  by  the  cation 
is  therefore 


107.93 


y 

107.93 


W'y _ 

X  107.93 


W 


A 


107.93 
and  the  fraction  carried  by  the  anion  is 


TJ7/  v         X 

y_          X  107.93  I 
"J 


107.93 


107.93 


W 


107.93 


OF  THE 


**?x 

E  \ 

I    UNIVERSITY    1 

OF  J 

'^gturtg&S  .. 


CHAPTER  XIII. 

MEASUREMENT  OF  DIELECTRIC  CONSTANTS  AND  RADIO- 
ACTIVITY. 

THE  method  about  to  be  described  is  due  to  Nernst  and 
is  unquestionably  the  most  satisfactory  for  the  physico-chemi- 
cal laboratory.  In  Fig.  97  let  /  be  a  small  induction  coil, 


FIG.  97. 

Wi  and  W2  two  non-inductive  resistances,  ct  and  c2  two  thor- 
oughly insulated  condensers  having  capacities  ct  and  c2 
respectively,  and  T  a  telephone.  The  condition  for  silence 
in  the  telephone  is 

Wl  :  TF2  =  c2 :  ct. 

If  we  make  W1  =  W2f  arranging  c2  as  an  adjustable  con- 
denser, this  method  enables  us  to  compare  the  capacity  ct  with 
another  and  hence  to  determine  the  dielectric  constant.  If  a 
is  the  capacity  of  the  "  measuring-condenser, "  Cj  the  capacity 
of  an  air-condenser  which  gives  a  minimum  sound  in  the 

219 


220  ELECTRICAL  MEASUREMENTS. 

telephone,  b  the  corresponding  value  when  the  condenser  is 
filled  with  an  insulating  rubLtance  of  which  the  dielectric 
constant  is  DX}  then  we  have 

_b_ 
a' 

This  method  gives  poor  results  or  fails  entirely  if  the 
substance  of  which  the  die'ectric  constant  is  sought  conducts 
even  slightly. 

It  is  possible,  however,  to  obtain  correct  values  for  poor 
conducting  substances  if  the  conductivity  of  the  condenser 
cx  is  compensated  by  inserting  a  like  conductivity  in  the 
measuring-condenser. 

If  the  conductivity  of  the  condenser  q  is  W 4,  then  the  con- 
dition for  r  ilence  in  the  telephone  is 

q  =  c2    and    TF3  =  W4. 

Apparatus. — The  arrangement  of  the  apparatus  is  shown 
in  Figs.  98  and  lOOa.  /  is  the  instruction  coil;  Wi  and  W2  two 
parallel  resistances ;  \V3  and  PF4  two  shunt  resistances ;  c\  and 
c-2  the  measuring-condensers;  c  the  vessel  for  containing  the 
liquid  under  investigation,  which  through  the  contacts  e\ 
and  e2  is  connected  first  to  c\  and  then  to  c^  To  insure  a  sharp 
tone-minimum  in  the  telephone  all  parts  of  the  apparatus  must 
be  carefully  insulated.  The  electrolytic  resistances  Wi  and 
TF2,  which  are  directly  connected  with  the  induction  appa- 
ratus, conrkt  of  two  vertical  glass  tubes  about  13  cm.  long 
and  0.5  cm.  in  diameter,  each  provided  with  well-blackened 
platinum  electrodes,  the  upper  electrodes  being  adjustable. 

The  electrolytic  resistance  consists  of  the  following 
solution: 

Mannite 181  grams 

Boric  acid 62     " 

Water..  ,  1500     " 


DIELECTRIC  CONSTANTS  AND  RADIOACTIVITY.      221 

This  solution  is  chosen  because  of  its  very  small  tempera- 
ture coefficient. 

The  measuring-condenrer  consists  of  two  strong  rectangu- 
lar brass  plates  8  cm.  wide  and  12  cm.  long.  The  capacity 


FIG.  98. 

was  increased  through  inserting  a  glass  plate  provided  with 
a  vernier. 

For  compensation  within  wider  limits  the  additiona 
shunt-resistances  W3  and  W4  are  included  in  the  circuit 
parallel  to  the  measuring-condenser. 

This  shunt-resistance,  Fig.  99,  consists  of  a  narrow  tube 
rv  and  a  wide  tube  r?  into  the  lower  end  of  which  is  fused  an 
electrode  e.  The  positions  of  the  other  electrodes  in  rt  and 
r2  can  be  adjusted  by  means  of  a  ccrew  and  divided  scale. 

The  liquid  to  be  invertigated  io  placed  in  the  measuring- 
vessel.  This  is  shown  in  Fig.  100,  The  capacity  of  the 


222 


ELECTRICAL  MEASUREMENTS. 


vessel  was  determined,  as  in  the  determination  of  resistances, 
by  calibration  with  a  liquid  of  known  dielectric  constant. 
The  following  liquids  are  well  adapted  to  the  purpose : 

D 

Ether 4.12 

Benzene..  .  2.258 


FIG.  99. 


The  small  telephone .  must  be  provided  with  a  well-insu- 
ated  handle. 


FIG.  100. 

Carrying  Out  a  Determination.— The  determination  of 
the  dielectric  constant  by  the  Nernrt  method  divides  itself 
into  three  parts: 

(1)  Establishment  of  the  Equality  of  Resistances  }^\  and  W2. — 
The.  vessel  C  and  the  resistances  W3  and  TF4  are  removed 


DIELECTRIC   CONSTANTS  AND   RADIOACTIVITY.       223 

and  TFj  and  W 2  are  tested  for  equality  by  adjusting  the 
measuring-condensers  until  the  minimum  in  the  telephone 
is  obtained.  The  connections  are  then  changed  so  that  W2 
is  connected  with  C\  and  W  \  is  connected  with  (72,  Then  the 
resistances  Wl  and  W2,  and  also  the  condensers,  are  each 
slightly  altered  and  the  minimum  is  again  obtained.  This 
process  is  continued  until  no  further  change  in  the  adjust- 
ment of  the  condensers  is  necessary. 

(2)  Calibration  of  the  Measuring-condenser. — The  empty 
measuring-vessel  is  brought  to  such  a  capacity  by  means  of  a 
small  glass  plate  of  proper  thickness  (about  1  mm.)  that  by 
connecting  it  to  e2  it   is  necessary  to  draw  out   the   con- 
denser c2  about  1  cm.     The  left-hand  condenser  is  displaced 
to  the  minimum  position  while  the  right-hand  stands  at  0; 
the  measuring-vessel  is  then  connected  at  e2  and  the  resulting 
alteration  of  the  right-hand  condenser  is  measured.     Then  the 
measuring-vessel  is  placed  in  the   middle   between   el  and 
e2,  the   left-hand   condenser  put   in    while    the  right-hand 
stands  at  1,  the  vessel  again  added,  etc.,  etc.     If  the  right- 
hand  condenser  is  without  error  of  calibration,  the  addition 
of  the  vessel  must  always  correspond  with   an  equal  dis- 
placement (say  1  cm.) ;  from  the  deviations,  the  corrections 
for  the  scale  divisions  are  at  once  obtained.     The  values  of 
the  scale  divisions  of  the  left-hand  condenser  are  then  de- 
termined through  direct   comparison  with   the   right-hand 
condenser. 

(3)  Determination  of  the  Dielectric  Constant. — The  empty 
vessel  C  is  placed  in  the  middle  between  et  and  e2)  the  right- 
hand  condenser  placed  at  0,  and  the  left  adjusted  until  the 
minimum  in  the  telephone  is  obtained.     The  shunt-resistances 
W3  and  TF4  are  then  altered  until  the  telephone  minimum  is 
rendered  as  sharp  as  possible.    With  liquids  of  slight  con- 
ductivity one  should  use  only  the  narrow  resistance-tube. 


224  ELECTRICAL  MEASUREMENTS. 

The  vessel  C  is  connected  with  e2,  the  right-hand  condenser 
plate  adjusted  until  the  minimum  is  again  obtained.  This 
gives  the  condenrer  netting,  s2. 

The  same  measurement  is  repeated  with  the  vessel  C 
connected  to  e±.  This  gives  the  condenser  Eetting  sx.  The 
vessel  C  is  now  filled  with  the  calibration  liquid,  and  the  con- 
denser settings  o2  and  o^  with  the  right-  and  left-hand  con- 
denrers  are  obtained. 

The  vessel  is  then  filled  with  the  liquid  to  be  investigated, 
and  in  exactly  the  same  manner  the  positions  s2  and  s1  are 
obtained.  If,  owing  to  the  conductivity  of  the  liquid,  the 
telephone  minimum  ceares  to  be  sharp,  this  may  be  restored 
through  adjustment  of  the  shunt-resistances  W3  or  W4. 

The  dielectric  constant  is  calculated  from  the  data  experi- 
mentally obtained,  thus: 

D=      -  +l 


where  D  =  dielectric  constant  of  liquid; 

D0  =  dielectric  constant  for  calibration-liquid; 

o       |  _,  o 

s  =   2    '  1  =  position  of  measuring-condenser  for  the 

Zi 

empty  veccel  (7. 

o=  2      l  =  position  of  meacuring-condenr  er  for  the 
vessel  C  filled  with  calibration-liquid; 

or      I     or 

S  =  ~~^  —  ^^porition  of  measuring-condenr  er  for  the 
61 

vessel  C  filled  with  liquid  under  inver;tigation. 

According  to  Maxwell's  theory  the  index  of  refraction  is 
equal  to  the  square  root  of  the  dielectric  constant,  or 


DIELECTRIC  CONSTANTS   AND   RADIOACTIVITY.        225 

This  relation  has  been  shown  to  hold  very  satisfactorily. 
Nernst  has  pointed  out  that  the  greater  the  die'ectric  con- 
stant the  greater  the  dissociating  power.  That  this  is  of 
more  than  limited  application  may  be  seen  by  a  comparison 
of  tables  of  dissociating  power  of  solvents  and  their  dielectric 
constants. 

Measurement  of  Radioactivity. — The  methods  employed 
in  the  measurement  of  radioactivity  are  for  the  most  part 
based  upon  the  property  possessed  by  radioactive  sub- 
stances of  rendering  the  air  a  conductor  of  electricity.  This 
conductivity  is  due  to  the  production  of  positive  and  negative 
ions  which  serve  as  carriers  of  the  electric  charge.  In  order 
to  compare  the  radiations  from  different  radioactive  sub- 
stances, it  is  essential  that  the  electric  field  be  of  sufficient 
strength  to  obtain  the  maximum  current  through  the  gas. 
This  current  is  known  as  the  saturation  current.  The  field 
intensity  required  to  produce  saturation  varies  with  the 
radioactivity  of  the  substances  under  examination.  For 
specimens  of  radium  having  very  high  activity  it  is  im- 
possible to  obtain  a  sufficiently  high  voltage  to  insure  satura- 
tion without  considerable  inconvenience.  The  method  to 
be  used  in  the  measurement  of  radiocativity  thus  depends 
upon  the  activity  of  the  specimens  to  be  examined. 

In  the  majority  of  cases,  however,  we  are  dealing  with 
comparatively  low  activities  or  with  such  small  quantities 
of  active  material  that  no  difficulty  is  experienced  in  obtain- 
ing the  saturation  current. 

The  Electroscope. — The  micro-electroscope  of  C.  T.  R. 
Wilson  is  a  highly  satisfactory  instrument  for  the  comparison 
of  radioactivities. 

The  essential  part  of  this  instrument  is  shown  in  Fig.  101 
while  Fig.  102  shows  the  assembled  apparatus. 


226  ELECTRICAL  MEASUREMENTS. 


FIG.  lOOa. 


FIG.  101. 


FIG.  102 


DIELECTRIC  CONSTANTS  AND  RADIOACTIVITY.      227 

In  a  brass  vessel  VV  there  is  suspended  a  gold-leaf 
system,  consisting  of  a  gold-leaf  E  attached  to  a  flat  strip 
of  brass  D,  which  is  supported  by  the  rod  A  through  the 
small  bead  of  sulphur  S.  The  sulphur  is  employed  because 
of  its  excellent  insulating  properties.  By  means  of  a  light 
brass  rod  BC  passing  through  the  ebonite  cover  FF,  the 
gold-leaf  system  can  be  charged  from  a  battery  of  200  or 
300  volts. 

The  charging  rod  BC  is  then  turned  about  a  vertical  axis 
so  as  to  leave  the  system  insulated,  and  the  rods  A  and  B 
and  the  vessel  VV  are  connected  to  the  earth. 

The  rate  of  collapse  of  the  gold-leaf  is  measured  by  means 
of  a  reading  microscope  through  two  mica  windows  in  the 
vessel.  The  eye-piece  of  the  microscope  is  furnished  with  a 
suitable  scale  for  reading  the  angular  position  of  the  gold- 
leaf. 

The  substance  under  examination  is  placed  beneath  the 
.gold-leaf  system,  the  radiations  thus  ionizing  the  air  between 
D  and  E. 

In  carrying  out  a  measurement  with  the  micro-electro- 
scope the  system  is  first  charged  with  the  battery  as  directed 
above,  and  the  apparatus  tested  for  leakage.  If  the  sulphur 
bead  be  dry  and  the  metal  cylinder  GG  be  connected  with 
the  earth,  the  leakage  is  so  small  that  for  ordinary  measure- 
ments no  account  need  be  taken  of  it.  The  small  leakage 
that  may  take  place  over  the  sulphur  bead  can  be  com- 
pletely eliminated  by  keeping  the  rod  A  charged  to  the  average 
potential  of  the  system  during  an  observation. 

Equal  quantities  of  finely  divided  uranium  oxide  and 
the  radioactive  preparation  are  then  weighed  out  in  similar 
shallow  glass  vessels  and  the.  preparations  are  spread  evenly 
over  the  bottoms  of  each  receptacle. 

The  uranium  oxide  is  placed  on  the  supporting  table  at  a 


228  ELECTRICAL  MEASUREMENTS. 

definite  distance  below  the  gold-leaf  system,  and  the  time  is 
noted  that  the  gold-leaf  takes  to  move  over  a  fixed  number 
of  divisions.  The  system  is  then  recharged  and  the  radio- 
active preparation  is  put  on  the  table  in  place  of  the  uranium 
oxide  and  the  time  of  fall  through  the  same  number  of  scale 
divisions  is  noted.  Since  the  capacity  of  the  charged  system 
remains  constant,  the  average  rate  of  fall  is  directly  propor- 
tional to  the  ionization  current  or  to  the  intensity  of  radiation 
emitted. 

This  type  of  apparatus  being  uninfluenced  by  electro- 
static disturbances  in  the  room  is  frequently  much  superior 
to  other  forms.  Perhaps  its  greatest  usefulness  is  in  the 
study  of  the  highly  penetrating  radiations  from  radioactive 
materials  which  readily  pass  through  the  walls  of  the  elec- 
troscope. 

In  the  study  of  this  type  of  radiations  the  electroscope 
is  placed  on  a  plate  of  lead  3  or  4  mms.  thick,  the  ionization 
then  observed  being  entirely  attributable  to  the  very  pene- 
trating rays,  since  the  a  and  /?  rays  are  absorbed  by  the 
lead. 

The  Electrometer. — While  the  electroscope  has  decided 
advantages  over  other  forms  of  apparatus  for  certain  measure- 
ments yet  it  is  of  limited  application,  and  the  greater  number 
of  determinations  of  ionization  currents  are  made  with  the 
electrometer. 

A  very  satisfactory  instrument  is  that  devised  by  Dole- 
zalek.  This  instrument  shown  in  Fig.  103  has  a  needle  of 
light  silvered  paper  and  a  very  fine  quartz  suspension  which 
is  made  a  conductor  by  coating  it  with  a  trace  of  calcium 
chloride.  The  sensitiveness  is  so  great  that  it  is  only  neces- 
sary to  keep  the  needle  at  a  potential  of  50  to  200  volts. 

Since  the  sensitiveness  passes  through  a  maximum  as 
the  potential  is  raised  it  is  advisable  to  make  a  practice  of 


DIELECTRIC  CONSTANTS  AND  RADIOACTIVITY.      229 

charging  the  needle  to  the  critical  potential  each  time  the 
instrument  is  used.  Another  point  in  favor  of  this  form 
of  electrometer  is  that  the  needle  lies  so  close  to  the  quad- 
rants that  it  is  self-damping,  thus  avoiding  the  necessity  of 
adding  any  damping  device. 


FIG.  103. 


It  is  important  in  the  adjustment  of  the  electrometer 
to  see  that  the  needle  is  symmetrically  placed  with  regard 
to  the  four  quadrants.  This  can  be  tested  for  by  noting 
whether  there  is  any  deflection  on  charging  the  needle,  the 
quadrants  all  being  connected  with  the  earth.  If  this  con- 
dition is  satisfied,  the  zero  reading  remains  constant  as  the 


230  ELECTRICAL  MEASUREMENTS. 

needle  loses  its   charge  and  the  deflection  for  equal  and 
opposite  charges  has  the  same  numerical  value. 

It  is  advisable  before  using  the  electrometer  to  test  it  for 
leakage.  To  this  end  the  system  is  charged  to  a  potential 
sufficient  to  give  a  deflection  of  about  200  scale  divisions. 

If  after  standing  for  one  minute  the  needle  does  not 
move  more  than  two  divisions,  the  insulation  may  be  con- 
sidered satisfactory.  With  an  instrument  as  sensitive  as  the 
Dolezalek  electrometer  it  is  essential  that  it  and  the  testing 
apparatus  should  be  completely  enclosed  in  a  wire  screen 
which  is  connected  to  the  earth.  This  precaution  avoids 
trouble  from  electrostatic  disturbances  in  the  vicinity  of  the 
apparatus.  If  the  testing  apparatus  is  at  some  distance 
from  the  electrometer  it  is  also  a  good  plan  to  enclose  the 
wires  in  lead  tubing  which  is  connected  with  the  earth. 

The  presence  of  gas  flames  is  also  a  source  of  disturbance, 
which  is  to  be  avoided  whenever  accurate  measurements 
are  to  be  made.  It  is  also  worthy  of  mention  that  accurate 
measurements  cannot  be  made  in  a  room  where  radioactive 
material  has  been  prepared  for  any  length  of  time,  since 
the  walls  and  furnishings  of  the  room  become  radioactive. 

Testing  Vessel. — A  convenient  form  of  testing  vessel  is 
shown  in  Fig.  104.  It  consists  of  a  metal  vessel  VV  inside 
of  which  are  the  parallel,  insulated  metal  plates  A  and  B. 

The  plate  A  is  connected  with  the  battery,  the  plate  B 
with  the  earth,  while  the  vessel  is  also  connected  with  the 
earth. 

The  vessel  is  provided  with  a  door  not  shown  in  the 
diagram  through  which  the  material  to  be  tested  is  introduced. 

The  plate  A  is  provided  with  a  shallow  depression  about 
2  mm.  deep  and  5  cm.  square  in  which  the  material  under 
test  is  placed  and  evenly  spread  out.  By  means  of  a  metal 
strip  N  on  one  of  the  ebonite  supports  connection  with  the 


DIELECTRIC  CONSTANTS  AND  RADIOACTIVITY.      231 

batteiy  is  permanently  established,  thus  avoiding  the  trouble 
of  disconnecting  every  time  the  plate  A  is  removed. 


FIG.  104. 

Battery. — For  measurements  of  radioactivity  it  is  neces- 
sary to  have  at  one's  command  a  source  of  E.M.F.  of  about 
300  volts. 

This  is  best  secured  through  a  battery  of  small  accumu- 
lators of  capacity  of  about  f  ampere  hour. 

Electrometer  Key. — A  very  satisfactory  key  for  electro- 
meter measurements  is  shown  in  Fig.  105.  A  stout  metal 
support  A  has  a  brass  tube  B  attached  to  one  end  while  the 
other  end  is  firmly  fixed  to  the  table  and  connected  with 
the  earth. 

Through  B  passes  a  brass  rod  C  which  is  supported  by  a 
string  D.  Below  B  is  a  mercury  cup  E  into  which  the  rod 
C  may  be  lowered  and  by  means  of  which  earth  connec- 
tion is  established  with  the  electrometer  and  the  testing 
vessel. 

When  the  string  is  pulled  the  earth  connection  of  the 
electrometer  and  testing  vessel  is  broken. 


232 


ELECTRICAL  MEASUREMENTS. 


Electrometer         Testing'Vessel  Earth 


Earth 


FIG.  106. 


Eartk 


Ea  th, 


DIELECTRIC  CONSTANTS  AND  RADIOACTIVITY.      233 

Measurement  of  the  lonization  Current.  —  To  measure 
the  current  between  the  plates  of  the  testing  vessel  the 
apparatus  is  connected  as  shown  in  Fig.  106,  where  B  is 
the  battery,  E  the  electrometer,  K  the  key,  and  DGGC  is 
the  testing  vessel.  By  means  of  the  key  the  plate  D  and 
the  pair  of  quadrants  connected  with  it  are  insulated,  and 
if  the  positive  terminal  of  the  battery  is  connected  with  the 
plate  C  the  plate  D  and  the  electrometer  commences  to 
acquire  a  positive  charge.  As  the  potential  of  D  begins  to 
rise  the  electrometer  needle  commences  to  move  at  a  uniform 
rate,  and  if  sufficient  time  be  given  the  potential  of  D  will 
eventually  be  nearly  equal  to  that  of  C.  The  movement 
of  the  needle  is  best  observed  by  means  of  a  telescope  and 
scale  and  the  rate  of  deflection  is  measured  by  means  of  a 
stop-watch,  noting  the  time  required  for  the  needle  to  pass 
through  100  scale  divisions.  This  rate  of  movement  of  the 
needle  is  taken  as  a  measure  of  the  current  through  the 
gas. 

When  the  observation  is  completed  the  key  is  lowered 
and  connection  with  the  earth  is  re-established. 

In  this  measurement  as  with  the  measurements  with  the 
micro-electroscope  the  material  examined  should  be  com- 
pared with  a  standard  sample  of  uranium  oxide.  The  radia- 
tions from  a  sample  of  uranium  oxide  are  very  constant  and 
the  same  saturation  current  may  be  obtained  from  it  over 
long  intervals  of  time. 

The  current  in  amperes  in  the  electrometer  circuit  is 
given  by  the  formula, 

.         Cd 


where  C  is  the  capacity  of  the  electrometer  and  connections 
in  electrostatic  units,  d  the  number  of  scale  divisions  passed 


234  ELECTRICAL  MEASUREMENTS. 

over  per  second,  and  D  the  sensibility  of  the  electrometer 
measured  in  scale  divisions  for  a  potential  difference  of 
1  volt  between  the  quadrants.  For  the  methods  of  measuring 
the  capacity  of  the  electrometer  some  laboratory  manual 
of  physics  should  be  consulted. 


DYNAMICAL  MEASUREMENTS. 
CHAPTER  XIV. 

SOLUBILITY. 

BY  the  term  solubility  we  understand  the  extent  to 
which  one  substance  dissolves  in  another. 

The  study  of  solubility  is  of  great  importance  in  many 
physico-chemical  investigations. 

Though  nine  different  classes  of  solutions  may  be  dis- 
tinguished, the  one  most  frequently  studied  is  the  solution  of 
a  solid  in  a  liquid.  When  a  solid  substance  is  dissolved  by 
a  liquid  there  is  formed  a  homogeneous  mixture  which  is 
inseparable  by  mechanical  means.  When  the  liquid  has 
taken  up,  at  a  definite  temperature,  all  the  solid  that  it  can 
the  solution  is  said  to  be  saturated. 

In  general  there  are  two  methods  of  obtaining  saturated 
solutions. 

(1)  The  finely  powdered  solid  is  brought  into  the  liquid 
and  agitated  for  some  time  at  a  definite  temperature,  until 
no  more  is  dissolved. 

(2)  The  solution  is  made  as  in  (1),  only  at  a  higher  tem- 
perature than  that  to  which  it  is  ultimately  reduced. 

In  both  of  these  methods,  which  give  the  same  result  if 
carefully  executed,  the  same  general  rule  holds  that  in  order 
for  a  solution  to  be  saturated,  it  must  always  be  in  contact  with 
the  solid  substance.  In  making  a  saturated  solution  the 
suggestion  put  forth  by  Ostwald  is  valuable:  "  It  is  best  to 
rub  up  a  little  of  the  substance  with  a  few  drops  of  the  sol- 
vent, and  then  add  so  much  of  the  magma  to  the  almost 

235 


236 


DYNAMICAL    MEASUREMENTS. 


saturated  solution  that  a  cloudy  liquid,  which  only  clears 
up  on  long  standing,  is  produced.7' 

One  of  the  most  satisfactory  arrangements  for  the  de- 
termination of  solubility  has  been  devised  by  Noyes,  a 
sketch  of  which  is  shown  hi  Fig.  107, 


D 


FIG.  107. 

AA  is  a  large  water-bath  on  the  bottom  of  which  is 
placed  an  elongated  glass  bulb,  B,  the  neck  of  which  rises 
up  by  the  wall  of  the  bath  and  is  bent  over  horizontally 
above.  This  is  then  connected  with  an  Ostwald  gas-regu- 
lator, C.  The  Ostwald  gas-regulator  (Fig.  108)  consists  of  a 
U  tube,  the  bend  of  which  contains  mercury,  while  the  two 
arms  are  connected  respectively  v/ith  the  bulb  in  the  bath 
and  with  the  gas-supply.  The  gas  enters  through  A,  which 
is  inserted  into  one  arm  of  the  U  tube  and  is  moved  down 
until  it  nearly  touches  the  mercury.  In  the  side  of  A  there 
is  a  very  small  hole  which  prevents  the  flame  under  the 
bath  being  extinguished  when  the  lower  end  of  A  is  closed 
by  the  expansion  of  the  liquid  in  B.  When  the  bath 
cools  the  liquid  in  B  (a  10%  solution  of  CaCl2)  contracts, 


SOLUBILITY.  237 

the  mercury  in  the  regulator  falls,  and  more  gas  is  ad- 
mitted to  the  burner.  By  proper  adjustment  it  thus  be- 
comes possible  to  regulate  the  temperature  of  the  bath  auto- 
matically. 

Upon  the  shaft  DD  are  fastened  the  vessels  containing 
the  solutions  together  with  some  of  the  finely  divided  solid, 
and  by  means  of  a  hot-air  engine  or  other  motor  the  shaft 


PIG.  108. 

is  made  to  revolve.  In  this  way  the  vessels  containing  the 
solutions  can  be  kept  in  continuous  agitation. 

Determination  of  Solubility.  —  The  thermostat  is  ad- 
justed for  the  desired  temperature,  the  shaft  DD  being 
slowly  revolved  to  insure  complete  uniformity  of  tempera- 
ture throughout  the  liquid.  The  vessels  E  are  filled  with 
the  solutions,  care  being  taken  to  have  present  some  of  the 
solid.  The  vessels  should  be  closed  with  rubber  stoppers, 
since  they  are  more  water-tight  than  ground-glass  stoppers. 
They  are  then  fastened  in  the  yokes  on  the  shaft,  and  the 
motor  started. 

At  temperatures  above  40°  C.  less  than  an  hour  is  suffi- 
cient to  complete  the  saturation,  provided  the  agitation  is 
vigorous.  For  lower  temperatures  much  longer  times  will 
be  necessary. 

When  saturation  is  complete   the  motor  is  stopped,  the 


238 


DYNAMICAL  MEASUREMENTS. 


vessels  are  removed  and  their  contents  allowed  to  settle. 
Of  course  the  vessels  containing  the  solutions  must  be  kept 
in  the  thermostat,  otherwise  some  solid  would  either  sepa- 
rate or  pass  into  solution  according  as  the  room  tempera- 
ture was  below  or  above  that  of  the  bath. 


FIG.  109 


FIG.  110. 


When  the  solutions  have  settled  the  quantity  necessary 
for  analysis  is  taken  from  the  clear  portion  by  means  of  a 
pipette.  At  high  temperatures  there  is  danger  of  loss  due 
to  evaporation  of  the  solvent.  The  pipette  shown  in  Fig. 
109  is  used  for  removing  the  liquid.  The  pipette  is  weighed 
before  and  after  removing  the  liquid,  the  contents  being 
washed  out  for  analysis.  The  analysis  may  be  effected 
either  by  evaporation  and  direct  weighing  of  the  dissolved 


SOLUBILITY.  239 

substance  or  by  gravimetric  or  volumetric  methods.  The 
application  of  physical  methods,  such  as  the  determination 
of  the  density  or  the  electrical  conductivity,  may  be  of  ser- 
vice in  ascertaining  the  composition  of  the  solution. 

The  expression  of  the  results  of  the  analysis  may  be  either 
in  terms  of  100  parts  of  solvent  or  100  parts  of  solution. 
The  latter  method,  proposed -by  Etard,  has  the  advantage  that 
the  curves  representing  solubility  as  a  function  of  tempera- 
ture are  usually  straighter,  and  great  solubilities  are  more 
conveniently  expressed  since  they  cannot  exceed  100.  Sub- 
stances which  contain  water  of  crystallization  should  be  cal- 
culated in  the  anhydrous  state. 

.Another  form  of  solubility  apparatus  which  has  been 
used  by  Van't  Hoff  is  shown  in  Fig:  110. 

By  means  of  a  hot-air  motor  or  a  turbine  the  stirrer  AB 
is  driven.  This  stirrer  is  carried  by  means  of  the  glass  tube 
(7;  the  rod  D  along  the  axis  allows  the  liquid  to  flow  out 
when  saturation  is  attained  through  a  plug  of  glass  wool,  F, 
into  the  weighing-tube  E.  The  whole  arrangement  is  obvi- 
ously to  be  immersed  in  the  thermostat. 

Partition  of  a  Solute  between  Two  Non-miscible  Solvents. 
—If  a  substance  be  subjected  to  the  simultaneous  solvent- 
action  of  two  non-miscible  solvents,  the  extent  to  which 
it  will  dissolve  in  each  is  dependent  upon  (1)  the  tempera- 
ture, (2)  the  solubility  in  each  solvent  taken  separately, 
and  (3)  its  molecular  weight  in  each  solvent.  The  ratio 
of  the  concentrations  in  each  solvent  is  known  as  the  parti- 
tion coefficient. 

Two  cases  are  here  to  be  distinguished:  (1)  when  the 
solute  has  the  same  molecular  weight  in  each  solvent  and 
(2)  when  the  molecular  weight  in  each  solvent  is  different. 

In  determining  a  partition  coefficient  the  apparatus 
shown  in  Fig.  107  is  found  useful.  In  one  of  the  bottles 


240  DYNAMICAL  MEASUREMENTS. 

place  100  cc.  of  a  solution  of  the  solute  in  one  of  the  solvents, 
the  concentration  of  the  solution  being  known.  To  this 
is  added  100  cc.  of  the  other  solvent.  The  bottle  is  then 
tightly  stoppered  and  placed  in  one  of  the  yokes  on  the 
shaft  DD  in  the  thermostat  and  the  solution  is  shaken  for 
30  or  40  minutes.  The  bottle  is  then  removed  from  the 
yoke  and  is  placed  upright  in  the  thermostat  until  the  solu- 
tions have  separated  into  two  distinct  layers.  By  means 
of  a  pipette  portions  of  each  layer  are  removed  and  the 
concentration  of  the  solute  in  each  is  determined  analytically. 

This  process  should  be  repeated  for  different  concentra- 
tions and  at  different  temperatures. 

If  the  solute  has  the  same  molecular  weight  in  each 
solvent,  then  the  partition  coefficient  will  be  expressed  by 
the  ratio 

Cl 


If,  on  the  other  hand,  there  be  association,  the  solute 
having  a  normal  molecular  weight  in  one  solvent  and  a 
multiple  of  this  in  the  other,  then  the  ratio  will  no  longer 
be  a  constant. 

The  condition  in  the  second  case  is  given  by  the  equa- 
tion, 


Applying  the  law  of  mass  action  to  this  equation  we  find 
that 


n  — 

Vc2 


If  in  determinations  of  this  character  we  have  to  deal 
with  electrolytes  we  find  that  the  partition  coefficient  de- 


SOLUBILITY.  241 

parts  from  a  constant  value  as  the  solutions  become  more 
dilute. 

This  deviation  is  due  to  dissociation  of  the  electrolyte. 
In  a  similar  manner  the  breaking  down  of  the  molecular 
complexes  in  cases  where  the  solute  does  not  possess  normal 
molecular  weight  in  solution  gives  rise  to  a  lack  of  constancy 
in  the  partition  coefficient. ' 


CHAPTER  XV. 

CHEMICAL  KINETICS. 
FROM  the  law  of  mass  action  the  general  reaction 


may  be  written 


Since  the  velocity  of  a  reaction  is  proportional  to  its 
constant,  K,  the  total  velocity  is  equal  to  the  algebraic  sum 
of  the  velocities  in  the  two  directions,  or 


If  the  concentration  of  the  substance  being  formed  is 
increased  by  dc  in  the  time  dt,  then 


...  -  K'c/"1  '< 


Since  the  constants  K  and  Kr  are  functions  of  the  tem- 
perature, it  follows  that  the  above  equation  holds  only  when 

the  reaction  is  isothermal. 

242 


CHEMICAL  KINETICS.  243 

If  there  are  present  four  substances  initially,  that  is,  at 
<=0,  and  the  respective  concentrations  are  a1}  a2,  a/,  a2', 
and  x  molecules  of  at  and  a2  are  decomposed  at  the  time  t, 
then 


This  equation  may  be  very  much  simplified  since  most 
reactions  are  nearly  complete  in  one  direction,  so  that  the 
second  term  may  be  omitted  and  we  may  write 


Chemical  reactions  are  divided  into  orders,  the  order  of  a 
reaction  being  determined  by  the  number  of  substances 
which  undergo  change.  It  has  been  found  by  experiment 
that  there  is  no  chemical  reaction  of  higher  order  than  the 
third. 

Reaction  of  the  First  Order.  —  The  equation  for  a  first- 
order  reaction  is 


which  upon  integration  gives 

T.    1  .         a 
K=-log£  -  . 
t      *sa—x 

Inversion  of  Cane-sugar.  —  The  reaction 


is  an  example  of  this  type  of  reaction,  the  only  substance 
undergoing  change  being  the  cane-sugar,  since  the  water  is 
present  in  such  large  excess  that  its  mass  remains  practically 
unchanged. 


244  DYNAMICAL  MEASUREMENTS. 

A  solution  of  cane-sugar  is  prepared  by  dissolving  200 
grams  of  sugar  in  distilled  water  and  diluting  to  1000  c.c. 
The  solution  is  then  filtered  into  a  clean,  dry  bottle  and 
warmed  in  the  thermostat  to  25°  C.  A  normal  solution  of 
pure  hydrochloric  acid  is  also  prepared  and  warmed  to  25°  in 
the  thermostat. 

The  Lippich  polarimeter  is  made  ready  and  the  polarizing 
tube  warmed  to  25°  by  circulating  water  at  that  temperature 
through  the  jacket.  The  polarization-tube  is  carefully  cleaned 
and  dried  and  one  of  the  plates  is  screwed  on,  then  10  c.c.  of 
the  sugar  solution  is  mixed  with  10  c.c.  of  the  acid,  the 
mixture  is  poured  into  the  tube  and  the  other  plate  screwed 
on,  taking  precautions  to  exclude  air-bubbles.  The  tube  is 
then  placed  in  the  polarimeter  and  observations  are  com- 
menced. During  the  first  stages  of  the  inversion,  readings 
are  taken  every  minute  until  five  readings  have  been  taken, 
the  mean  of  which  is  taken  as  the  time  of  the  third  reading. 

The  readings  are  then  taken  every  thirty  minutes  for  five 
hours,  after  which  the  solution  is  allowed  to  stand  for  a  period 
of  time  ten  times  as  great  as  that  required  for  half-inversion 
of  the  sugar,  when  the  final  reading  is  taken. 

If  /?!  and  /?2  are  the  rotations  corresponding  to  the  times 
^  and  t2}  and  <p  represents  the  constant  final  rotation,  then 


a  formula  which  can  readily  be  reconciled  with  the  equation 
for  a  first-order  reaction.  The  constant  for  the  above  20% 
solution  of  sugar  mixed'  with  an  equal  volume  of  normal 
hydrochloric  acid  at  25°  C.  is  0.00205. 

The  acid  is  added  for  the  purpose  of  accelerating  the 
velocity  of  the  reaction  through  the  catalytic  action  of  its 
hydrogen  ions. 


CHEMICAL  KINETICS.  245 

Cataly_is  of  Methyl  Acetate.  —  Another  first-order  reac- 
tion illustrating  the  catalytic  action  of  hydrogen  ions  is  the 
following: 

CH3  •  COOCH3 + H20  -  CH3COOH + CH3  -  OH. 

N 
There  is  first  prepared  an  approximately  ^Q  solution  of 

barium  hydroxide,  and  after  this  has  been  carefully  stand- 

N 
ardized  -^  solutions   of  hydrochloric,  nitric,  and  sulphuric 

z 

acids  are  made  up.  A  series  of  25-c.c.  bottles  are  then  thor- 
oughly cleaned  and  steamed,  and  each  is  furnished  with  a 
numbered  or  lettered  paraffined  stopper. 

Each  bottle  is  weighted  with  lead  so  that  it  can  be  wholly 
immersed  in  the  thermostat.  Into  each  bottle  is  introduced 
20  c.c.  of  semi-normal  acid  and  then  the  bottles  are  placed  in 
the  thermostat  at  25°.  When  the  contents  of  the  bottles  has 
acquired  the  temperature  of  the  thermostat  1  c.c.  of  pure, 
dry  methyl  acetate  is  added  and  the  mixture  thoroughly 
shaken.  Immediately  after  shaking  1  c.c.  is  removed  and 

N 

titrated  with  the  ^  barium  hydroxide,  the  time  being  noted 
zo 

when  the  first  drop  of  the  barium  hydroxide  comes  in  contact 
with  the  solution.  This  is  taken  as  the  initial  time  of  the 
reaction. 

At  intervals  of  twenty  minutes  for  two  hours,  and  then  at 
longer  intervals,  other  portions  are  removed  and  titrated,  the 
bottles  being  kept  continuously  in  the  thermostat.  A  small 
residue,  say  10  c.c.,  is  kept  at  the  constant  temperature  of 
25°  for  three  days  and  is  then  removed  and  titrated.  This 
last  titration  gives  the  final  reading  for  the  solution. 

If  a0  is  the  number  of  cubic  centimetres  of  barium  hydrox- 
ide initially  required  and  av  a2 .  .  .  an  the  quantities  required 


246  DYNAMICAL  MEASUREMENTS. 

at  successive  titrations,  and  A  is  the  final  quantity,  which  is  a 
constant  when  equilibrium  is  attained,  then 

(A-a0)-log(A-gn) 

A  —  lOg  , 

in 

where  t  is  the  time  expressed  in  minutes. 

This  formula  also  can  be  easily  reconciled  with  the  first- 
order  reaction. 

N 
The  constant  for  ^HCl  and   1  c.c.  of    CH3COOCH3  is 

0.0013  at  25°. 

Reaction   of   the   Second   Order.  —  -  The    equation   for    a 
second-order  reaction  is 


which  upon  integration  gives 


t   a(a—x)' 
Saponification  of  Ethyl  Acetate. — The  reaction 

CH3COOC2H5+Na;OH=CHsCOO,Na+C2H6OH 

is  a  typical  reaction  of  the  second  order. 

N 
To  study  this  reaction  we  first  prepare  a  ^  solution  of 

sodium    hydroxide    (free    from    carbonate),     standardizing 
against  succinic  acid. 

N 

A  ~~  aqueous  solution  of  chemically  pure,  dry  ethyl  ace- 
tate is  then  prepared,  the  ester  being  weighed  directly.  The 
flasks  or  bottles  containing  these  solutions  are  well  stoppered 
and  placed  in  the  thermostat  at  25°  for  several  hours.  When 


CHEMICAL  KINETICS.  247 

the  solutions  have  acquired  the  temperature  of  the  thermostat 
50  c.c.  of  each  solution  are  introduced  into  a  flask,  pre- 
viously warmed  to  25°,  and  the  mixture  vigorously  shaken. 
For  the  experiment  10  c.c.  of  the  mixture  is  measured  out 

N 

and  placed  under  a  burette  containing  -^  hydrochloric  acid, 

oU 

phenolphthalei'n  being  added  as  an  indicator.  Four  seconds 
before  the  initial  time  the  stop-cock  of  the  burette  is  opened 
and  the  acid  allowed  to  flow  in  until  within  10%  of  that 
required  for  neutralization.  This  requires  approximately, 
eight  seconds.  In  the  next  ten  seconds  the  exact  quantity 
of  acid  required  for  neutralization  can  be  determined.  As  an 
alternative  an  excess  of  acid  may  be  run  in  at  first  and  then 
titrated  back  with  alkali  afterward. 

From  the  remainder  of  the  mixture,  successive  portions 
are  withdrawn  and  titrated  in  a  similar  manner  at  intervals 
of  5  minutes. 

Finally  10  c.c.  of  the  mixture  is  heated  to  100°  for  thirty 
minutes,  and  when  cool  is  titrated  as  above.  This  gives  the 
excess  of  sodium  hydroxide  over  the  ester,  when  equilibrium 
has  been  attained.  For  equilibrium  we  have 

log  at  +  log  (a0  -  a,)  -  log  a0-  log  (at  -  ae) 

A  = , 

aet 

where  a^  is  the  number  of  cubic  centimetres  of  hydrochloric 
acid  required  to  neutralize  the  mixture  initially,  at  is  the 
quantity  of  acid  required  at  any  time  t  reckoned  from  the 
initial  titration,  and  ae  is  the  number  of  cubic  centimetres  of 
acid  required  in  the  final  titration. 

Transition  Points. — It  is  found  that  the  crystalline  form 
of  a  polymorphous  substance  is  in  general  a  function  of  the 
temperature. 

The  temperature  at  which  two  different  crystalline  modi- 


248  DYNAMICAL  MEASUREMENTS. 

fications  can  remain  in  equilibrium  is  known  as  the  transition 
temperature  or  transition  point.  Transition  points  are 
found  not  only  in  the  case  of  polymorphous  substances, 
but  also  in  the  case  of  hydrated  salts.  A  definite  hydrate 
being  stable  up  to  a  certain  temperature  beyond  which  a 
hydrate  of  different  composition  is  the  stable  form. 

Of  the  several  methods  in  use  for  the  determination  of 
transition  points,  all  are  not  equally  adapted  to  every  case 
and  each  may  give  slightly  different  values. 

The  following  methods  will  be  outlined  here:  (1)  Solu- 
bility, (2)  thermometric,  (3)  tensimetric,  (4)  dilatometric, 
and  (5)  electrical. 

Solubility  Method. — The  solubility  of  the  polymorphous 
substance  or  hydrate  is  determined  as  directed  in  the  chapter 
on  solubility,  care  being  taken  to  make  the  measurements 
at  temperatures  differing  by  not  more  than  two  degrees 
as  the  transition  point  is  approached. 

At  temperatures  near  the  transition  point  the  solid 
phase  should  be  separated  from  the  solution  as  rapidly  as 
possible  by  filtration,  then  dried  between  sheets  of  filter- 
paper  and  the  number  of  molecules  of  water  of  crystalliza- 
tion determined  by  the  usual  analytical  method. 

The  results  should  be  plotted  on  coordinate  paper,  tem- 
peratures as  abscissae  and  solubilities  as  ordinates.  It  will 
be  found  that  each  hydrate  has  its  own  solubility  curve, 
the  point  of  intersection  being  the  transition  point.  The 
solubility  curves  for  Na2S04 .  10H20  and  Na2S04  are  shown 
in  Fig.  111.  ABC  being  the  solubility  curve  for  the  deca- 
hydrate  and  EBD  the  curve  for  the  anhydrous  salt. 

Thermometric  Method. — It  is  found  that  the  change 
from  one  form  to  another  is  always  accompanied  by  a  thermal 
change,  heat  being  absorbed  or  evolved.  To  measure 
accurately  the  thermal  change  taking  place  in  such  a  trans- 


TRANSITION  POINTS. 


formation,  requires  a  relatively  large  amount  of  the  substance. 
The  apparatus  used  in  this  method  is  shown  in  Fig.  112. 


a  o 

s  a 


About  40  grams  of  the  hydrate  are  placed  in  the  test  tube 
A,  comple  ely  surrounding  the  bulb  of  the  thermometer  0. 
The  tube  A  is  then  placed  in  a  beaker  of  water  BB  the 


250 


DYNAMICAL  MEASUREMENTS. 


temperature  of  which  is  slowly  raised  by  means  of  a  small 
Bunsen  flame.  It  is  desirable  to  have  a  stirrer  in  the  beaker 
to  insure  uniformity  throughout  the  bath. 


FIG.  112. 


When  the  hydrate  begins  to  melt  the  temperature  of  the 
bath  is  kept  constant  and  the  contents  of  the  test-tube  is 
stirred  by  means  of  the  stirrer  D,  the  thermometer  being 
read  at  frequent  intervals.  The  temperature  of  the  bath 


TRANSITION  POINTS.  251 

is  now  increased  at  the  rate  of  about  one  degree  for  every 
five  minutes  and  the  thermometer  C  is  read  regularly  at 
intervals  of  one  minute. 

This  slow  increasing  of  the  temperature  of  the  bath  should 
be  continued  beyond  the  transition  temperature  and  the 
thermometer  readings  should  be  recorded,  the  contents  of 
A  being  stirred  constantly.  .  When  the  transition  point  has 
been  passed  then  the  flame  is  removed  from  the  bath  and 
the  system  is  allowed  to  cool  slowly,  the  stirring  and  read- 
ing of  the  thermometer  being  continued  until  the  tempera- 
ture is  well  below  the  transition  point.  Two  curves  are  now 
plotted  on  coordinate  paper,  one  for  rising  temperatures 
and  the  other  for  falling  temperatures. 

In  each  of  these  curves  times  are  plotted  as  abscissae 
and  temperatures  as  ordinates.  It  will  be  found  that  each 
.curve  has  an  approximately  horizontal  portion  correspond- 
ing to  the  transition  temperature.  Some  difficulty  may  be 
experienced  in  this  method  owing  to  suspended  transforma- 
tion, but  this  can  be  avoided  by  dropping  into  A  a  small 
piece  of  the  stable  solid  phase. 

Tensimetric  Method. — In  this  method  use  is  made  of 
the  fact  that  when  two  hydrates  are  in  equilibrium  at  their 
transition  point,  their  vapor  pressures  become  equal.  In 
Fig.  113  is  shown  a  sketch  of  the  Bremer-Frowein  tensi- 
meter  which  is  very  satisfactory  in  measurements  of  this 
character.  It  is  essentially  a  differential  manometer,  the 
two  limbs  of  the  U-tube  AB  being  brought  close  together 
over  the  millimeter  scale.  The  bend  of  the  tube  is  filled 
with  some  liquid  suitable  for  indicating  small  pressures, 
while  the  substances  of  which  the  relative  vapor  pressures 
are  sought,  are  placed  in  the  small  flasks  E  and  F.  The 
necks  of  E  and  F  are  then  sealed  off,  the  apparatus  is  inclined 
so  as  to  permit  the  liquid  in  the  manometer  to  flow  into  the 


252 


DYNAMICAL  MEASUREMENTS. 


bulbs  D  and  C  and  then  G  is  connected  with  an  exhaust 
pump  and  the  tensimeter  is  exhausted  and  sealed  at  G. 
The  apparatus  is  then  placed  in  a  vertical  position  in  a 
thermostat,  and  when  equilibrium  has  been  established  the 
level  of  the  liquid  in  A  and  B  is  read  on  the  millimeter  scale. 


FIG.  113. 


The  temperature  of  the  thermostat  is  then  raised  and  a 
new  reading  is  obtained.  This  is  continued  over  the  desired 
range  of  temperature  the  results  being  plotted  on  coordi- 
nate paper,  taking  temperatures  as  abscissae  and  differences 
of  level  as  ordinates. 


TRANSITION  POINTS. 


253 


Dilatometric  Method. —  In  this  method  advantage  is 
taken  of  the  fact  that  changes  in  crystalline  form  or  com- 
position are  accompanied  by  appreciable  changes  in  volume. 
To  ascertain  at  what  temperatures  these  volume  changes 
take  place  use  is  made  of  an  instrument  known  as  a  dila- 


,A 

FIG.  114. 


tometer  (Fig.  114).  This  consists  of  a  bulb  B  sealed  to  a 
long  capillary  tube  D  which  carries  a  millimeter  scale  C, 
either  etched  on  the  stem  of  the  dilatometer  or  attached 
to  the  capillary  tube  as  shown  in  the  illustration. 

A  portion  of  the  substance  under  investigation  is  placed 
in  the  bulb  B  through  the  open  end  A,  which  is  then  sealed 
off.  The  remainder  of  the  bulb  and  part  of  the  capillary 


254  DYNAMICAL  MEASUREMENTS. 

are  filled  with  some  liquid  which  is  without  action  upon  the 
substance. 

The  dilatometer  is  now  placed  in  a  vertical  position  in  a 
thermostat,  the  temperature  of  which  is  below  that  of  the 
transition  point.  When  the  dilatometer  has  acquired  the 
temperature  of  the  thermostat  the  position  of  the  meniscus 
is  noted  and  the  temperature  of  the  bath  is  increased  very 
slowly,  the  height  of  the  meniscus  being  read  for  each  degree 
rise  of  the  bath.  So  long  as  no  transformation  takes  place 
the  rate  of  expansion  will  be  nearly  uniform,  but  when  the 
transition  point  is  reached  there  will  be  a  sudden  increase 
per  degree,  if  the  change  be  accompanied  by  increase  of 
volume,  or  a  sudden  decrease  if  the  transformation  be  accom- 
panied by  a  diminution  of  volume.  After  the  transition 
point  has  been  passed  the  change  in  volume  again  becomes 
uniform. 

On  allowing  the  bath  to  cool  similar  changes  take  place 
in  the  reverse  direction.  The  results  should  be  plotted 
on  coordinate  paper,  taking  temperatures  as  abscissae  and 
volumes  as  ordinates.  Owing  to  suspended  transformation 
the  curve  obtained  for  falling  temperatures  may  not  coincide 
with  the  curve  obtained  for  rising  temperatures. 

Electrical  Method. — This  method  is  of  limited  appli- 
cability, but  where  it  can  be  employed  it  gives  excellent 
results. 

It  is  due  to  Cohen  who  employed  it  in  studying  the 
system. 

ZnS04  .  7H20  <=>  ZnS04  6H20  +  H20. 

It  depends  upon  the  fact  that  an  electromotive  force  is 
set  up  by  the  difference  in  concentration  of  the  zinc  ions 
on  two  sides  of  a  cell,  one  side  of  which  contains  the  hexa- 
hydrate  and  the  other  side  the  hepta-hydrate. 


TRANSITION  POINTS. 


255 


The  arrangement  for  a  measurement  of  this  kind  is  shown 
in  Fig.  115,  where  A  and  B  are  the  two  sides  of  the  experi- 
mental cell,  R  is  a  variable  resistance,  K  a  key,  and  G  a 
sensitive  D'Arsonval  galvanometer  with  mirror  and  scale. 

Each  side  of  the  cell  is  filled  with  saturated  solutions 
of  the  hepta-hydrate,  A  being  kept  for  some  time  above 
the  transition  point  until  the  hepta-hydrate  has  passed  over 
into  hexa-hydrate.  The  two  sides  of  the  cell  are  then  con- 


FIG.  115. 

nected,  and  the  whole  is  placed  in  the  thermostat  TT,  which 
has  been  adjusted  to  maintain  a  temperature  a  few  degrees 
below  the  transition  temperature.  The  temperature  is 
gradually  raised,  the  galvanometer  being  read  at  intervals 
of  two  minutes.  As  the  transition  temperature  is  approached, 
the  E.M.F.  becomes  less  and  the  galvanometer  readings  are 
consequently  smaller.  When  the  transition  temperature 
is  reached  the  concentration  of  the  zinc  ions  on  each  side 
is  the  same  and  consequently  the  E.M.F.  becomes  zero. 
This  method  has  been  extended  by  Cohen,*  and  full  details 
may  be  found  in  the  literature. 

*  "  Studies  in  Chemical  Dynamics." — Van't  Hoff-Cohen. 


TABLES. 


I. 

REDUCTION  TO  VACUUM  OF  WEIGHINGS  MADE  WITH  BRASS 
WEIGHTS  IN  AIR. 


8 

k 

s 

k 

s 

k 

0.7 

+  1.57 

2.0 

+  0.457 

8 

+  0.007 

0.8 

1.36 

2.5 

0.337 

9 

-0.010 

0.9 

1.19 

3.0 

0.257 

10 

-0.023 

.0 

1.06 

3.5 

0.200 

11 

-0.034 

.1 

0.95 

4.0 

0.157 

12 

-0.043 

.2 

0.86 

4.5 

0.124 

13 

-0.051 

.3 

0.78 

5.0      . 

•0.097 

14 

-0.057 

.4 

0.71 

5.5 

0.075 

15 

-0.063 

.5 

0.66 

6.0 

0.057 

16 

-0.068 

.6 

0.61 

6.5 

0.042 

17 

-0.072 

.7 

0.56 

7.0 

0.029 

18 

-0.076 

.8 

0.52 

7.5 

0.017 

19 

-0.080 

1.9 

0.49 

8.0 

0.007 

20 

-0.083 

2.0 

0.46 

21 

-0.086 

II. 

DENSITY. 

SOLIDS. 


Aluminium 2.7 

Brass 8.1-8.7 

Copper 8.5-8.9 

Glass,  common 2 . 4-2 . 6 

"       flint 3.0-5.9 

Gold 19.3 

Ice 0.9167 

Indium 21 . 8-22 . 4 

Iron,  cast 7 . 1-7 . 7 

"      wrought 7.8 

"      steel 7.8 

LIQUIDS  (20°). 

Alcohol 0.789  Olive-oil.  ..  . 

Amyl  acetate 0 . 88  Petroleum .  . 

Carbon  bisulphide 1 . 264  Turpentine.  . 

Chloroform 1 . 489  Water,  pure. 

Ether 0.715  "       gey,.. 

Glycerine f 1 . 23  Mercury 

GASES  (0°  AND  760  MM.). 


Lead 11.3 

Nickel 8.8 

Platinum 21.4 

Quartz 2 . 65 

Silver 10.5 

Tin 7.3 

Zinc 7.1 

Wood,  pine 0.35-0.50 

oak 0.60-0.90 

"       cork..  0.2 


Air 0.001293 

Oxygen 0 . 001429 

Nitrogen 0 . 001 251 

Hydrogen 0.0000899 

Carbon  dioxide 0.001965 

Electrolytic  gas 0 . 000536 


Referred  to 
Air  =  l. 
1.0000 
1 . 1052 
0.9672 
0.06951 
1.520 
0.4148 


...  0.92 
...  0.88 
...  0.87 
...  0.998 
...   1  024 
..13.546 


Referred  to 
O  =  16. 
14.477 
16.000 
14.002 
1.007 
22.00 
6.00 
259 


260 


TABLES. 


III. 
DENSITY  OF  WATER. 


0° 

0.999823 

1 

0.999882 

2 

0.999923 

3 

0.999947 

4 

0.999955 

5 

0.999947 

6 

0.999923 

7 

0.999884 

8 

0.999831 

9 

0.999763 

10 

0.999682 

11 

0.999587 

12 

0.999480 

13 

0.999359 

14 

0.999226 

15 

0.999081 

16° 

0.998925 

17 

0.998756 

18 

0.998577 

19 

0.998387 

20 

0.998185 

21 

0.997974 

22 

0.997752 

23 

0.997520 

24 

0.997278 

25 

0.997026 

26 

0.996765 

27 

0.996496 

28 

0.996214 

29 

0.995926 

30 

0.995628 

rv. 

VOLUME  OF  WATER  FROM  0°  TO  31°. 


0° 

L.  000126 

1 

I.  000070 

2 

.000030 

3 

.000007 

4 

.000000 

5 

.000008 

6 

.000031 

7 

.000069 

8 

.000122 

9 

.000188 

10 

.000269 

11 

.000363 

12 

.000470 

13 

.000590 

14 

.000722 

15 

.000867 

16° 

.001025 

17 

.001193 

18 

.001373 

19 

.001564 

20 

.001768 

21 

.001981 

22 

.002204 

23 

.002438 

24 

.002681 

25 

.002935 

26 

.003199 

27 

.003472 

28 

.003788 

29 

.004045 

30 

.004346 

31 

.004656 

TABLES. 


261 


V. 

SURFACE  TENSION  OF  LIQUIDS  IN  CONTACT  WITH  AIR. 

Surface  Tension 
(Dynes  per  sq.  cm.). 

25.6 
30.2 
24  .  8 
28  .  8 
30  .  5 
28.3 
18.4 
63.  14 
470  .  0 
24.7 
34.7 
25.9 
20.1 
28.5 


T  ;n,,5ri 
Liquld' 

Acetone  ..................  '.  ........  14.0 

Acetic  acid  ........................  17.0 

Amyl  alcohol  ......................  15.0 

Benzene  ..........................  15.0 

Carbon  disulphide  ..................  20  .  0 

Chloroform  ........................  20.0 

Ether  .............................  20.0 

Glycerine  .........................  17.0 

Mercury  ..........................  20  .  0 

Methyl  alcohol  .....................  15.0 

Olive  oil  ..........................  20.0 

Petroleum  .........................  20.0 

Toluene  ...........................  15.0 

Turpentine  ........................  21.0 


IV. 

VISCOSITY  OF  LIQUIDS. 

Liquid.  Temp.  Viscosity  Coefficient. 

Ammonia 14.5  0.0149 

Glycerine 14.3  13.87 

20.3  8.30 

Mercury 20 . 0  0 . 0157 

Olive  oil 0  3 . 2653 

Petroleum 17.5  0.0190 

Rape-oil 20.0  1 .63 


262 


TABLES. 


VII. 
REDUCTION  OF  GAS  VOLUMES  TO  0°  AND  760  MM. 


v  =  volume; 


10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 


;     s=  density;      t=  temperature;      7/=pressui 

V 

H 

760 

V°     l+at 

760" 

s°='           ^  H 

l+at 

t 

l  +  at                            — 

mm. 

1.0367 

21 

1.0771 

700 

1.0404 

22 

1.0807 

710 

1.0440 

23 

1.0344 

720 

1.0477 

24 

1.0881 

730 

1.0514 

25 

1.0917 

740 

1  .  0550 

26 

1.0954 

750 

1.0587 

27 

1.0991 

760 

1.0624 

28 

1  .  1028 

770 

1.0661 

29 

1  .  1064 

780 

1.0697 

30 

1.1101 

790 

1.0734 

99 

1.3633 

800 

100 

1.3670 

810 

101 

1.3707 

820 

H 

760 

0.9211 
0.9342 
0.9474 
0.9605 
0.9737 
0.9868 
1.0000 
1.0132 
1.0263 
1.0395 
1.0526 
1.0658 
1.0789 


VIII. 

REDUCTION  OF  BAROMETER  READINGS  TO  0°. 
When  the  height  of  the  mercury  column  has  been  measured  with  a 
brass  scale,  the  length  of  which  is  correct  at  0°,  the  mercury  and  scale 
being  at  t°,  the  observed  height  is  reduced  to  0°  by  subtracting  the  value 
given  in  the  table  corresponding  to  the  temperature  and  height. 

Observed  Height  in  Centimetres. 


72 

73 

74 

75 

76 

77 

10 

0.12 

0.12 

0.12 

0.12 

0.12 

0.12 

11 

0.13 

0.13 

0.13 

0.13 

0.14 

0.14 

12 

0.14 

0.14 

0.14 

0.15 

0.15 

0.15 

13 

0.15 

0.15 

0.16 

0.16 

0.16 

0.16 

14 

0.16 

0.17 

0.17 

0.17 

0.17 

0.17 

15 

0.17 

0.18 

0.18 

0.18 

0.18 

0.19 

16 

0.19 

0.19 

0.19 

0.19 

0.20 

0.20 

17 

0.20 

0.20 

0.20 

0.21 

0.21 

0.21 

18 

0.21 

0.21 

0.22 

0.22 

0.22 

0.22 

19 

0.22 

0.22 

0.23 

0.23 

0.23 

0.24 

20 

0.23 

0.24 

0.24 

0.24 

0.25 

0.25 

21 

0.25 

0.25 

0.25 

0.25 

0.26 

0.26 

22 

0.26 

0.26 

0.26 

0.27 

0.27 

0.27 

23 

0.27 

0.27 

0.2S 

0.28 

0.28 

0.29 

24 

0.23 

0.28 

0.29 

0.29 

0.29 

0.30 

25 

0.29 

0.30 

0.30 

0.30 

0.31 

0.31 

TABLES. 


263 


IX. 

REDUCTION  OF  MERCURY-IN-GLASS  THERMOMETER 
ING  TO  THE  NORMAL  HYDROGEN  SCALE. 


READ- 


Reading. 

0° 
10 
20 
30 
40 
50 


FOR  JENA  NORMAL  GLASS. 


Correction. 
0°.000 


-0 
-0 
-0 
-0 


.055 
.090 
.109 
.115 


-0  .109 


Reading. 

50° 
60 
70 
80 
90 
100 


Correction. 

-0°.109 
-0  .096 
-0  .076 
-0  .053 
-0  .027 
0  .000 


X. 

CAPILLARY  DEPRESSION  OF  MERCURY. 
INTERPOLATED  BY  F.  KOHLRAUSCH  FROM  MENDELEJEFF  AND  GUTKOWSKY. 


Dia. 


Height  of  Meniscus  in  mm. 


0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

4 

0.83 

1.22 

1.54 

1.93 

2.37 

5 

0.47 

0.65 

0.86 

1.19 

1.45 

1.80 

6 

0.27 

0.41 

0.56 

0.78 

0.98 

1.21 

1.43 

7 

0.18 

0.28 

0.40 

0.53 

0.67 

0.82 

0.97 

1.13 

8 

0.20 

0.29 

0.38 

0.46 

0.56 

0.65 

0.77 

q 

0.15 

0.21 

0.23 

0.33 

0.40 

0.46 

0.52 

10 

0  15 

0  20 

0  25 

0  29 

0  33 

0  37 

11 

0  10 

0  14 

0  18 

0  21 

0  24 

0  27 

12 

0  07 

0  10 

0  13 

0  15 

0  18 

0  19 

13 

0  04 

0  07 

0  10 

0  12 

0  13 

0.14 

264 


TABLES. 


XI. 

VAPOR  PRESSURE  OF  WATER. 
FROM   -19°  TO  100°  IN  MILLIMETRES  OF  MERCURY. 


t. 


A. 


A, 


14 
13 
12 
11 


-10 
9 

o 
3 

7 
6 


19    l-029 
18    1.120    - 

n 

-,f> 

16 

ic 

10 


.562 

.694 
.836 


2.151 
2.327 


2'715 
2.930 


0.246 


2   3.950, 

1  4.249 

0°  4.569 

+    1  4.909 

2  5.272 

3  5.658 

4  6.069 

5  6.507 

6  6.972 
7 

8  7. 

9  8. 


o  4Q4 
u.tvt 
Q  (-9P 
W'OAW 
/-.  re7 
U.ODr 

0.592 


9.140 
9.767 


+  10 
11 

12  10.432 

13  11. 137  n 

14  11.884U 

15  12.674 

16  13.510,, 

17  14.395  X'SS? 

18  15.330  0'93j 

19  16.319  u< 


-7 
'ZS 

0-9C 


20 
21 
22 
23 
24 
25 
26 
27 
23 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 


17.3^3 

19^630 
20.858 
22.152 
23.517 
24.956 
26.471 
2^.065 
29.744 

31.51 
33.37 
35.32 
37.37 
39.52 
41.78 
44.16 
46.65 
49.26 
52.00 


.679 
1.77 

1  £A 


900 
*'** 


« 

287 


+  40 
41 
42 
43 
44 
45 
46 
47 
48 
49 

50 
51 
52 
53 
54 
55 
56 
57 
58 
59 


54.87 
57.87 


o 
™ 

' 


61  .  02 

64.31 

87.76 

71.3677 
75.132-2 
79.07  f^ 
83.19  T-lg 

87.49  ' 


91.93 
96.66 
101.55 
106.65 
111.  97 
117.52 
123.29 
129.31 
125.58 
142.10 


fjS 


60  148.88 

61  155.95 

62  163.29 

63  170.02 

64  178.86 

65  187.10 

66  195.67 

67  204.56 
6^  213.79 
69  223.37 


' 


+  70 
71 
72 
73 

1A 

74 

TK 

75 

76 

77 
7? 
79 


90 
91 
92 
93 
94 
95 
96 
97 
9-8 
99 


233.31 
243.62 
254.30 


OT«  v7 

2/6.67 

r)  >o  nr* 

2  SS.  76 

301.09 

313.85 
327.05 
340.73 


2  oo 


80  354.87 

81  369.51 

82  384.64 

83  400.29 

84  416.47 

85  433.19 

86  450.47 

87  468.32 

88  486.76 

89  505.81 


525.47 
545.77 
566.71  Sf'JE 
588.83  99?f 
610.64  £•£ 
633.66  SX'^ 
657.40  ;2'1J 
681.88  o?  or 
707.13 


788.18 


535 


TABLES. 


265 


XII. 

VAPOR  PRESSURE  OF  MERCURY 

IN  MILLIMETRES,  ACCORDING  TO  REGNAULT  AND  HERTZ  (a)  AND  RAMSAY 
AND  YOUNG   6. 


a.           b. 

a.           6. 

a.           b. 

a.          6. 

0°  0.0002    
10    0.0005   

100°  0.2  5  0.270 
110    0.470   

200°    18.25  17.02 
210      25.12 

300°  242.2  246.8 
310    299.7  304.8 

20    0.0013    
30    0.0029 

120   0.779  0.719 
130    1.24 

220      34.9     31.96 
230      45.4 

320   368.7  373.7 
330    450.9  454.4 

40    0.007     0.00  i 

140    1.93     1.763 

240      58.8 

340    548  4  548.6 

50    0.014     0015 

150    2.93 

250      75.8 

350    663.2  658.0 

60    0.02  >     0.0  9 

160    4.38     4.013 

260     96.7 

360    797.7       .    . 

70    0.051     0.052 

170    6.41 

270    123.0     123.9 

370    954.7 

80    0.093     0.093 

LSO    9.23     8.535 

280    155.2     157.4 

3V011397 

90    0.163     0.160 

19013.07     

290    194.5     19S.O 

3901346.7   

XIII. 
TABLE  FOR  THE  CONVERSION  OF  THERMOMETER  READINGS. 


Degrees  Centigrade X  1.8  +32=  degrees  Fahrenheit. 
Degrees  Fahrenheit  —32 

1.8 

Degrees  Reaumur  X  9 
~~ 


-+32 
<± 

Degrees  (Fahrenheit  -32)4 

9 
Degrees  Reaumur  X  5 

4 
Degrees  Centigrade  X  4 


=  degrees  Centigrade. 
=  degrees  Fahrenheit. 
=  degrees  Reaumur. 
=  degrees  Centigrade. 
=  degrees  Reaumur. 


266 


TABLES. 


XIV. 

SPECIFIC  HEATS,  HEATS  OF    FUSION,  AND  MELTING-POINTS 
OF  THE  ELEMENTS. 


Name. 

Specific 
Heat. 

Heat  of 
.Fusion. 

Melting- 
point  , 
Centigrade 

Authority  for 
Melting-points. 

Aluminium  . 

0   229 

80 

625 

R  oberts-  Austin 

Antimony.  . 

051 

16 

432 

Pouillet 

Bismuth. 

.031 

12  4 

268  3 

Rudberg 

Cadmium  

055 

13  1 

320  7 

Person 

Chromium  

100 

1515 

E.  A.  Lewis 

Cobalt  

107 

63 

1500 

Pictet 

Copp6r 

095 

43 

1054 

Violle 

Gold 

032 

16  3 

1045 

Violle 

Iridium 

033 

28 

1950 

Violle 

Iron,  wrought.  .  . 

112 

69 

1600 

Pictet 

Lead  

032 

5  4 

326  2 

Person 

Magnesium  
Manganese  

.245 
122 

58 

750 
1245 

Herapus 

Mercury  

032 

2  8 

-39  5 

Regnault 

Nickel  

108 

68 

1484 

Bredig 

Osmium  . 

031 

35 

2500 

Pictet 

Palladium. 

059 

36  3 

1587 

Bredig 

Platinum  

032 

27  2 

1780 

Bredig 

Rhodium  

058 

52 

2000 

Pictet 

Ruthenium  

061 

46 

2000+ 

Deville  &  Debray 

Silver  

057 

24  7 

961  5 

Bredig 

Tin  

056 

14  5 

232  7 

Person 

Titanium.  .  .  . 

113 

3000 

Tungsten.  .  . 

035 

1700 

Zinc  

096 

22  6 

419 

Bredig 

TABLES.  267 


XV. 

COEFFICIENTS  OF  EXPANSION,   SPECIFIC  HEATS,  MELTING- 
POINTS,  AND  BOILING-POINTS  OF  LIQUIDS. 

Coefficient  of            Specific  Melting-  Boiling- 
Expansion.                Heat.  point.  point. 

Ether 0.00163              0.54  -118°  34°. 9 

Alcohol 0.00110        .      0.58  -110  78.3 

Amyl  alcohol 0.00093               0.55  130  .0 

Aniline 0.00085               0.49  -     8  184.0 

Benzene 0.00024               0.40  +5  80.3 

Chloroform 0.00026               0.23  -   70  61  .2 

Acetic  acid 0.00007               0.50  +    17  118.0 

Glycerine 0.00050               0.58  -20  290.0 

Methyl  alcohol 0 . 00022               0 . 60  66  . 0 

Nitrobenzene 0.00085               0.34  +3  210.0 

Phenol 0.00084               +40  183  .0 

Toluene 0.00109               0.40  -102  110.0 

Water 0.00018               1  0  100.0 

Xylene 0.00101               0.40  +15  140.0 


XVI. 

BOILING  TEMPERATURE  t  OF  WATER  AT  BAROMETRIC 
PRESSURE  6. 

A_              _L  JL  L  b                L 

cm.  cm.  cm. 

72.0  98.49  74.0  99.26  76.0  100 

72.1  98.53  74.1  99.29  76.1  100.04 

72.2  98.57  74.2  99.33  76.2  100.07 

72.3  98.61  74.3  99.37  76.3  100.11 

72.4  98.65  74.4  99.41  76.4  100.15 

72.5  98.69  74.5  99.44  76.5  100.18 

72.6  98.72  74.6  99.48  76.6  100.22 

72.7  98.76  74.7  99.52  76.7  100.26 

72.8  98.80  74.8  99.55  76.8  100.29 

72.9  98.84  74.9  99.59  76.9  100.33 

73.0  98.88  75.0  99.63  77.0  100.37 

73.1  98.92  75.1  99.67  77.1  100.40 

73.2  98.95  75.2  99.70  77.2  100.44 

73.3  98.99  75.3  99.74  77.3  100.48 

73.4  99.03  75.4  99.78  77.4  100.51 

73.5  99.07  75.5  99.82  77.5  100.55 

73.6  99.10  75.6  99.85  77.6  100  58 

73.7  99.14  75.7  99.89  77.7  100.62 

73.8  99.18  75.8  99.93  77.8  100.66 

73.9  99.22  75.9  99.96  77.9  100.69 


268  TABLES. 

XVII. 

CORRECTION   FOR  TEMPERATURE   OF  MERCURY  IN 
THERMOMETER-STEM. 


t-t' 

70° 

80° 

90° 

100° 

120° 

140° 

160° 

180° 

200° 

220° 

10° 

0.02 

0.03 

0.05 

0.07 

0.11 

0.17 

0.21 

0.27 

0.33 

0.38 

20 

0.13 

0.15 

0.18 

0.22 

0.29 

0.38 

0.46 

0.53 

0.61 

0.67 

30 

0.24 

0.28 

0.33 

0.39 

0.48 

0,59 

0.70 

0.78 

0.88 

0.97 

40 

0.35 

0.41 

0.48 

0.56 

O.o8 

0.82 

0.94 

1.04 

1.16 

1.28 

50 

0.47 

0.53 

C.62 

0.72 

0.88 

1.03 

1.17 

1.31 

1.44 

1.59 

60 

0.57 

0.66 

0.77 

0.89 

1.09 

1.25 

1.42 

1.58 

1.74 

1  90 

70 

0.69 

0.79 

0.92 

.06 

1.30 

1.47 

1.67 

1.,'  6 

2.04 

2.23 

80 

0.80 

0.91 

1.05 

.21 

1.52 

1.71 

1.94 

2.15 

2.33 

2.55 

90 

0.91 

1.04 

1.19 

.38 

1.73 

1.96 

2.20 

2.42 

2.64 

2.89 

100 

1.02 

1.18 

1.35 

.56 

1.97 

2.18 

2.45 

2.70 

2.94 

3.23 

110 



.78 

2.19 

2.43 

2.70 

2.98 

3.26 

3.57 

120 

.98 

2.43 

2.69 

2.95 

3.26 

3.5S 

3.92 

130 

2  68 

2  94 

3  20 

3  53 

3  89 

4  28 

140 

2.92 

3  22 

3  47 

3  ;  6 

4  22 

4  64 

150 

3  74 

4  15 

4  56 

5  01 

160 

4  00 

4  48 

4  90 

5  39 

170 

4.27 

4.76 

5.24 

5.77 

180 

4.54 

5.07 

5.59 

6.15 

190 

5  33 

59"> 

6  54 

200 

r>  70 

6  30 

6  94 

210 

6  6  . 

7.35 

220 

-7.04 

7.75 

XVIII. 
WAVE-LENGTHS  OF  LINES  OF  SOLAR  SPECTRUM  IN  AIR  AT  1SC 


PRESSURE  760  MM.     UNIT  =  MICRON  =  0.001  MM. 


Line. 


Element. 


Wave-length 


A 

.... 

0.76280 

a 

0.71850 

B 

O 

0.68701 

C 

H       - 

0.65629 

a 

0 

0.62781 

A 

Na 

0.58960 

D* 

Na 

0.58900 

E 

Fe,Ca 

C.  52703 

bi 

Mg 

0.51837 

Li 

Wave-length 

C 

Fe 

0.49576 

F 

H 

0.48614 

d 

Fe 

0.46682 

e 

Fe 

0.43836 

f 

H 

0.43405 

G 

Fe,Ca 

0.43079 

h 

H 

0.41018 

H 

H,Ca 

0.39685 

K 

Ca 

0.39337 

TABLES. 


269 


XIX. 

TABLE  FOR  WHEATSTONE'S  BRIDGE, 
a 


l-o 


from  a=  0.001  to  0.999. 


a 

0 

1 

12 

3 

4 

5 

6 

7  ' 

8 

9 

00 

0.0000 

0010 

0020 

0030 

0040 

0050 

0060 

0071 

0081 

0091 

01 

0101  0111 

0122 

0132 

0142 

0152  0163 

0173 

0183 

0194 

02 

0204|  0215 

0225 

0235 

0246 

0256  0267 

0278 

0288 

0299 

03 

0309 

0320 

0331 

0341 

0353 

0363 

0373 

0384 

0395 

0406 

04 

0417 

0428 

0438 

0449 

0460 

0471 

0482 

0493 

0504 

0515 

05 

0526 

0537 

0549 

0560 

0571 

0582 

0593 

0605 

0616 

0627 

06 

0638 

0650 

0661 

0672 

0684 

0695  0707 

0718 

0730 

0741 

07 

0753 

0764 

0776 

0788 

0799 

0311 

OS23 

0834 

0846 

0858 

08 

0870 

0881 

0893 

0905 

0917 

0929 

0941 

0953 

0965 

0977 

09 

0989 

1001 

1013 

1025 

1038 

1050 

1062 

1074 

1087 

1099 

10 

0.1111 

1124 

1136 

1148 

1161 

1173 

1186 

1198 

1211 

1223 

11 

1236 

1249 

1261 

1274 

1287 

1299 

1312 

1325 

1338 

1351 

12 

1364 

1377 

1390 

1403 

1416 

1429 

1442 

1455 

1468 

1481 

13 

1494 

1508 

1521 

1534 

1547 

1561 

1574 

1.588 

1601 

1614 

14 

1628 

1641 

1655 

1669 

1682 

1696 

1710 

1723 

1737 

1751 

15 

1765 

1779 

1793 

1806 

1820 

1834 

1848 

1862 

1877 

1891 

16 

1905 

1919 

1933 

1947 

1962 

1976 

1990 

2005 

2019 

2034 

17 

0.2048 

2063 

2077 

2092 

2107 

2121 

2136 

2151 

2166 

2180 

18 

2195 

2210 

2225 

2240 

2255 

2270 

2285 

2300 

2315 

2331 

19 

2346 

2361 

2376 

2392 

2407 

2422 

2438 

2453 

2469 

2484 

20 

2500 

2516 

2531 

2547 

2563 

2579 

2595 

2610 

2626 

2642 

21 

2658 

2674 

2690 

2707 

2723 

2739 

2755 

2771 

2788 

2804 

22 

2821 

2S37 

2854 

2870 

2887 

2903 

2920 

2937 

2953 

2970 

23 

2987 

3004 

3021 

3038 

3055 

3072 

3089 

3106 

3123 

3141 

24 

0.3158 

3175 

3193 

3210 

3228 

3245 

3263 

3280 

3298 

3316 

25 

3333 

3351 

3369 

3387 

3405 

3423 

3441 

3459 

3477 

3495 

26 

3514 

3532 

3550 

3569 

3587 

3605 

3624 

3643- 

3661 

3680 

27 

3699 

3717 

3736 

3755 

3774 

3793 

3812 

3831 

3850 

3870 

28 

3889 

3908 

3928 

3947 

3967 

3986 

4006 

4025 

4045 

4065 

29 

0.4085 

4104 

4124 

4144 

4164 

4184 

4205 

4225 

4245 

4265 

270 


TABLES, 


XIX—  (Continued.} 
TABLE  FOR  WHEATSTONE'S  BRIDGE. 


a 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

30 

4286 

4306 

4327 

4347 

4368 

4389 

4409 

4430 

4451 

4472 

31 

4493 

4514 

4535 

4556 

4577 

4599 

4620 

4641 

4663 

4684 

32 

4706 

4728 

4749 

4771 

4793 

4815 

4837 

4.S59 

4881 

4903 

33 

4925 

4948 

4970 

4993 

5015 

503? 

5060 

5083 

5106 

5129 

34 

0.5152 

5175 

5198 

5221 

5244 

526'. 

5291 

5314 

5337 

5361 

35 

5385 

5408 

5432 

5456 

5480 

550± 

5528 

5552 

5576 

5601 

36 

5625 

5650 

5674 

5699 

5723 

5743 

5773 

5798 

5823 

5848 

37 

5873 

5h98 

5924 

5949 

5974 

6000 

6026 

6051 

6077 

(i!03 

38 

0.6129 

6155 

6181 

6208 

(3234 

6260 

6287 

6313 

6340 

6367 

39 

6393 

6420 

6447 

6475 

6502 

6529 

6556 

6584 

6611 

6639 

40 

6667 

6695 

6722 

6750 

6779 

6807 

6:35 

6863 

6S92 

6921 

41 

6949 

6978 

7007 

7036 

7065 

7094 

7123 

7153 

7182 

7212 

42 

0.7241 

7271 

7301 

7331 

7361 

7391 

7422 

7452 

7483 

7513 

43 

7544 

7575 

7606 

7637 

7668 

7699 

7731 

7762 

7794 

7825 

44 

7857 

7889 

7921 

7953 

7986 

8018 

8051 

8083 

8116 

8149 

45 

0.8182 

8215 

8248 

8282 

8315 

8349 

8382 

8416 

8450 

8484 

46 

8519 

8553 

8587 

8622 

8657 

8692 

8727 

8762 

8797 

8832 

47 

8868 

8904 

8939 

8975 

9011 

9048 

9084 

9121 

9157 

9194 

48 

0.9231 

9268 

9305 

9342 

9380 

9418 

9455 

9493 

9531 

9570 

49 

9608 

9646 

9685 

9724 

9763 

9802 

9841 

9881 

9920 

9960 

50 

1.000 

1.004 

1.008 

1.012 

.016 

1.020 

1.024 

1.028 

1.033 

1.037 

51 

1.041 

1.045 

1.049 

1.053 

.058 

1.062 

1.066 

1.070 

1.075 

1.079 

52 

1.083 

1.088 

1.092 

1.096 

.101 

1.105 

1.110 

1.114 

1.119 

1.123 

53 

1.128 

1.132 

1.137 

1.141 

.146 

1.151 

1.155 

1.160 

.165 

1.169 

54 

1.174 

1.179 

1.183 

1.188 

.193 

1.198 

1.203 

1.208 

.212 

1.217 

55 

1.222 

1.227 

1.232 

1.237 

1.242 

1.247 

1.252 

1.257 

.262 

1.268 

56 

1.273 

1.278 

1.283 

1.288 

1.294 

1.299 

1.304 

1.309 

.315 

1.320 

57 

1.326 

1.331 

1.336 

1.342 

1.347 

1.353 

1.358 

1.364 

.370 

1.375 

58 

1.381 

1.387 

1.392 

1.398 

1.404 

1.410 

1.415 

1.421 

.427 

1.433 

59 

1.439 

1.445 

1.451 

1.457 

1.463 

1.469 

1.475 

1.481 

.488 

1.494 

60 

1.500 

1.506 

1.513 

1.519 

1.525 

1.532 

1  .538 

1.545 

.551 

1.558 

61 

1.564 

1.571 

1.577 

1.584 

1.591 

1.597 

1.604 

1.611 

.618 

1.625 

62 

1.632 

1.639 

1.646 

1.653 

1.660 

1.667 

1.674 

1.681 

.688 

1.695 

63 

1.703 

1.710 

1.717 

1.725 

1.732 

1.740 

1.747 

1.755 

.762 

1.770 

64 

1.778 

1.786 

1.793 

1.801 

1.809 

1.817 

1.825 

1.833 

.841 

1.849 

TABLES. 


271 


XIX— (Continued.") 
TABLE  FOR  WHEATSTONE'S  BRIDGE. 


a 

0 

1 

2 

3 

4 

5 

6 

7 

8 

y 

65 

1.857 

1.8651  1.874 

1.882 

1.890  1.899 

1.907 

1.915 

1.924 

1.933 

66 

1.941 

1.950  1.959 

1.967 

1.976  1.985 

1.994 

2.003 

2.012 

2.021 

67 

2.030 

2.040  2.049 

2.058  2.067J  2.077 

2.086  2.096 

2.106 

2.115 

68 

2.125 

2.135  2.145 

2.155  2.165  2.175 

2.185  2.195 

2.205 

2.215 

69 

2.226 

2.236!  2.247 

2.257|  2.268  2.279 

2.289  2.300 

2.311 

2.322 

70 

2.333 

2.344  2.356 

2.367  2.378  2.390 

2.401   2.413 

2.425 

2.436 

71 

2.448 

2.460  2.472 

2.484  2.497  2.509 

2.521   2.534 

2.546 

2.559 

72 

2.571 

2.584!  2.597 

2.610  2.623 

2.636 

2.650  2.663 

2.676 

2.690 

73 

2.704 

2.717 

2.731 

2.745  2.759 

2.774)2.788  2.802 

2.817 

2.831 

74 

2.846 

2.861 

2.876 

2.891 

2.906 

2.922 

2.937!  2.953 

2.968 

2.984 

75 

3.000 

3.016 

3.032 

3.049  3.065 

3.082 

3.098 

3.115 

3.132 

3.149 

76 

3.167 

3.184 

3.202 

3.219  3.237 

3.255 

3.274  3.292 

3.310 

3.329 

77 

3.348 

3.367 

3.386 

3.405  3.425 

3.444 

1  3.464J  3.484 

3.505 

3.525 

78 

3.545 

3.566 

3.587 

3.608  3.630 

3.651 

3.673  3.695 

3.717 

3.739 

79 

3.762 

3.785 

3.808  3.831 

3.854 

3.878 

3.902  3.926 

3.950 

3.975 

80 

4.000 

4.025 

4.051  4.076 

4.102 

4.128 

4.155  4.181 

4.208 

4.236 

81 

4.263 

4.291 

4.319|  4.348 

4.376 

4.405 

4.435  4.465 

4.495 

4.525 

82 

4.556 

4.587 

4.618  4.650 

4.682  4.714 

4.747  4.780 

4.814 

4.848 

83 

4.882 

4.917 

4.952  4.988 

5.024  5.061 

5.098 

5.135 

5.173 

5.211 

84 

5.250 

5.289 

5.329  5.369 

5.410 

5.452 

5.494 

5.536 

5.579 

5.623 

85 

5.667 

5.711 

5.757 

5.803 

5.849 

5.897 

5.944 

5.993 

6.042 

6.092 

86 

6.143 

6.194 

6.246  6.299 

6.353 

6.407 

6.463 

6.519 

6.576 

6.634 

87 

6.692 

6.752!  6.813  6.874 

6.937 

7.000 

7.065 

7.130 

7.197 

7.264 

88 

7.333 

7.403  7.475  7.547 

7.621 

7.696 

7.772 

7.850 

7.929 

8.009 

89 

8.091 

8.174 

8.259  8.346 

8.434 

8.524 

8.615 

8.709 

8.804 

8.901 

90 

9.000 

9.101(9.204  9.309 

9.417 

9.526 

9.638 

9.753 

9.870 

9.989 

91 

10.11 

10.33 

10.36  10.49 

10.63 

10.77 

10.90 

11.05 

11.20 

11.35 

92 

11.50 

11.66 

11.82  11.99 

12.16 

12.33 

12.51 

12.70 

12.89 

13.08 

93 

13.29 

13.49 

13.71!  13.93 

14.15 

14.38 

14.63 

14.87 

15.13 

15.39 

94 

15.67 

15.95 

16.24  16.54 

16.86 

17.18 

17.52 

17.87 

18.23 

18.61 

95 

19.00 

19.41 

19.83 

20.28 

20.74 

21.22 

21.73 

22.26 

22.81 

23.39 

96 

24.00 

24.64 

25.32 

26.03 

26.78 

27.57 

28.41 

29.30 

30.25 

31.26 

97 

32.33 

33.48 

34.71 

36.04 

37.46 

39.00 

40.67 

42.48 

44.45 

46.62 

98 

49.00 

51.6 

54.6 

57.8 

61.5 

65.7 

70.4 

75.9 

82.3 

89.9 

99 

99.0 

110 

124 

142 

165 

199 

249 

332 

499 

999 

272 


TABLES. 


XX. 

TABLE  FOR  CALCULATING  THE  DISSOCIATION  CONSTANT. 

k  =  ,™~    ,  from  m  =  0.001  to  0.0999  and 

l=m 


from 


0.100  to  0.999. 


m 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.010 

1010 

1030 

1051 

1072 

1093 

1114 

1136 

1157 

1179 

1201 

11 

1223 

1246 

1268 

1291 

1315 

1337 

1361 

1385 

1408 

1433 

12 

1457 

1482 

1507 

1532 

1557 

1582 

1608 

1633 

1659 

1686 

13 

1712 

1739 

1765 

1792 

1820 

1847 

1875 

1903 

1931 

1959 

14 

1987 

2016 

2045 

2074 

2104 

2133 

2163 

2193 

2223 

2253 

15 

2284 

2314 

2345 

2376 

2408 

2440 

2473 

2505 

2537 

2569 

16 

2602 

2365 

2668 

2706 

2734 

2768 

2802 

2836 

2871 

2905 

17 

2940 

2975 

3010 

3046 

3081 

3118 

3154 

3190 

3226 

3262 

18 

3299 

3336 

3373 

3411 

3449 

3487 

3525 

3563 

3602 

3641 

19 

3680 

3719 

3758 

3798 

3838 

3878 

3918 

3958 

3999 

4040 

0.020 

4082 

4123 

4164 

4206 

4248 

4290 

4333 

4376 

4418 

4461 

21 

4505 

4548 

4591 

4635 

4680 

4724 

4759 

4813 

4858 

4903 

'  22 

4949 

4994 

5041 

5087 

5133 

5179 

5226 

5273 

5320 

5367 

23 

5415 

5462 

5510 

5558 

5607 

5655 

5704 

5753 

5802 

5852 

24 

5902 

5952 

6002 

6052 

6103 

6154 

6204 

6256 

6307 

6358 

25 

6410 

6462 

6514 

6567 

6619 

6672 

6725 

6778 

6832 

6886 

26 

6940 

6995 

7049 

7104 

7159 

7213 

7269 

7324 

7380 

7436 

27 

7492 

7548 

7605 

7662 

7719 

7777 

7834 

7892 

7949 

8007 

28 

8066 

8124 

8183 

8242 

8301 

8360 

8420 

8478 

8538 

8599 

29 

8661 

8721 

8782 

8844 

8905 

8966 

9028 

9090 

9152 

9215 

0.030 

9278 

9341 

9404 

9467 

9531 

9595 

9659 

9723 

9788 

9852 

31 

9917 

9982 

1005 

1011 

1017 

1025 

1031 

1038 

1044 

1051 

32 

1057 

1063 

1070 

1077 

1084 

1091 

1098 

1104 

1111 

1118 

33 

1125 

1132 

1138 

1146 

1153 

1160 

1167 

1174 

1181 

1188 

34 

1196 

1204 

1212 

1219 

1226 

1233 

1241 

1248 

1255 

1263 

35 

1270 

1277 

1285 

1292 

1300 

1307 

1314 

1322 

1330 

1337 

36 

1345 

1352 

1360 

1368 

1375 

1383 

1391 

1398 

1406 

1414 

37 

1422 

1430 

1438 

1446 

1454 

1462 

1470 

1478 

1486 

1494 

38 

1502 

1510 

1518 

1526 

1534 

1543 

1551 

1559 

1567 

1575 

39 

1583 

1592 

1600 

1608 

1616 

1625 

1633 

1642 

1650 

1658 

TABLES. 


273 


TABLE  FOR  CALCULATING  THE  DISSOCIATION  CONSTANT. 

Continued. 


m 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.040 

1667 

1675 

1684 

1692 

1701 

1710 

1718 

1727 

1736 

1744 

41 

1753 

1762 

1770 

1779 

1788 

1797 

1805 

1814 

1823 

1832 

42 

1841 

1850 

1859 

1868 

1877 

1886 

1895 

1904 

1913 

1922 

43 

1932 

1941 

1950 

1959 

1968 

1978 

1987 

1996 

2005 

2015 

44 

2024 

2034 

2043 

2053 

2062 

2071 

2081 

2090 

2100 

2110 

45 

2119 

2129 

2139 

2149 

2159 

2168 

2178 

2188 

2198 

2208 

46 

2217 

2227 

2237 

2247 

2257 

2267 

2277 

2287 

2297 

2307 

47 

2317 

2327 

2337 

2347 

2357 

2368 

2379 

2389 

2399 

2409 

48 

2420 

2430 

2440 

2450 

2461 

2471 

2482 

2492 

2503 

2513 

49 

2524 

2534  !  2545 

2555 

2566 

2577 

2587 

2599 

2610 

2620 

0.050 

2631 

2642  ,  2653 

2663 

2674 

2685 

2696 

2707 

2718 

2729 

51 

2741 

2752  2763 

2774 

2785 

2796 

2807 

2818 

2829 

2840 

52 

2852 

2863  2874 

2885 

2897 

2908 

2919 

2931 

2942 

2953 

53 

2965 

2977 

2989 

3000 

3012 

3023 

3035 

3047 

3058 

3070 

54 

3081 

3093 

3105 

3116 

3128 

3140 

3152 

3164 

3176 

3187 

55 

3199 

3211 

3223 

3235 

3248 

3260 

3272 

3284 

3296 

3308 

56 

3321 

3333 

3345 

3357 

3370 

3383 

3395 

3407 

3419 

3432 

57 

3444 

3457 

3469 

3481 

3494 

3507 

3520 

3532 

3545 

3558 

58 

3570 

3583 

3595 

3608 

3621 

3634 

3647 

3660 

3673 

3686 

59 

3699 

3711 

3724 

3737 

3751 

3764 

3777 

3790 

3803 

3816 

0.060 

3830 

3843 

3856 

3870 

3883 

3896 

3910 

3923 

3936 

3950 

61 

3963 

3977 

3990 

4004 

4017 

4030 

4044 

4057 

4071 

4084 

62 

4098 

4111 

4125 

4139 

4153 

4166 

4180 

4194 

4208 

4222 

63 

4236 

4250 

4264 

4278 

4292 

4306 

4320 

4334 

4348 

4362 

64 

4376 

4391 

4405 

4419 

4434 

4448 

4462 

4477 

4491 

4505 

65 

4519 

4534 

4548 

4563 

4577 

4592 

4606 

4621 

4635 

4650 

66 

4664 

4679 

4694 

4708 

4723 

4738 

4752 

4767 

4782 

4796 

67 

4811 

4826 

4841 

4856 

4871 

4886 

4901 

4916 

4931 

4946 

68 

4961 

4976 

4992 

5007 

5023 

5036 

5054 

5069 

5085 

5100 

69 

5115 

5130 

5146 

5161 

5177 

5192 

5208 

5223 

5239 

5254 

0.070 

5269 

5284 

5300 

5316 

5331 

5347 

5362 

5378 

5394 

5410 

71 

5426 

5442 

5458 

5474 

5490 

5506 

5522 

5538 

5554 

5570 

72 

5586 

5602 

5619 

5636 

5652 

5668 

5685 

5701 

5717 

5733 

73 

5749 

5766 

5782 

5799 

5815 

5832 

5848 

5865 

5881 

5898 

74 

5914 

5931 

5947 

5964 

5981 

5997 

6014 

6031 

6047 

6064 

75 

6081 

6098 

6115 

6132 

6149 

6166 

6183 

6200 

6217 

6234 

76 

6251 

6268 

6286 

6303 

6320 

6338 

6355 

6372 

6390 

6407 

77 

6424 

6442 

6459 

6477 

6494 

6512 

6529 

6547 

6564 

6582 

78 

6599 

6617 

6634 

6652 

6670 

6687 

6705 

6723 

6740 

6758 

79 

6776 

6794 

6812 

6829 

6847 

6865 

6883 

6901 

6919 

6937 

274 


TABLES. 


TABLE  FOR  CALCULATING  THE  DISSOCIATION  CONSTANT. 

Continued. 


m 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.080 

6955 

6973 

6992 

7010 

7029 

7047 

7066 

7084 

7103 

7121 

81 

7139 

7158 

7176 

7197 

7215 

7234 

7252 

7270 

7288 

7307 

82 

7325 

7344 

7362 

7381 

7400 

7418 

7437 

7456 

7475 

7494 

83 

7513 

7532 

7551 

7570 

7589 

7608 

7627 

7646 

7665 

7684 

84 

7703 

7722 

7741 

7761 

7780 

7799 

7819 

7838 

7857 

7876 

85 

7896 

7916 

7935 

7955 

7975 

7994 

8014 

8033 

8053 

8072 

86 

8092 

8112 

8131 

8151 

8171 

8190 

8210 

8230 

8250 

8270 

87 

8290 

8310 

8330 

8350 

8370 

8391 

8411 

8431 

8451 

8471 

88 

8491 

8511 

8532 

8552 

8572 

8593 

8613 

8633 

8654 

8674 

89 

8695 

8715 

8736 

8757 

8777 

8798 

8819 

8839 

8860 

8881 

0.090 

8901 

8922 

8942 

8963 

8984 

9005 

9026 

9047 

9068  ,  9089 

91 

9110 

9131 

9152 

9173 

9195 

9216 

9237 

9258 

9280 

9301 

92 

9322 

9343 

9365 

9386 

9408 

9429 

9451 

9472 

9494 

9515 

93 

9536 

9557 

9579 

9601 

9622 

9644 

9666 

9687 

9709 

9731 

94 

9753 

9775 

9796 

9818 

9840 

9862 

9884 

9906 

9928 

9950 

95 

9972 

9994 

1002 

1004 

1006 

1008 

1011 

1013 

1015 

1017 

96 

1020 

1022 

1024 

1027 

1029 

1031 

1033 

1036 

1038 

1040 

97 

1042 

1044 

1047 

1049 

1051 

1054 

1056 

1058 

1060 

1063 

98 

1065 

1067 

1069 

1072 

1074 

1076 

1079 

1081 

1083 

1086 

99 

1088 

1090 

1092 

1095 

1097 

1099 

1101 

1104 

1106 

1109 

0.10 

1111 

1135 

1159 

1183 

1207 

1232 

1257 

1282 

1308 

1333 

11 

1360 

1386 

1413 

1440 

1467 

1494 

1522 

1550 

1579 

1607 

12 

1636 

1666 

1695 

1725 

1755 

1786 

1817 

1848 

1879 

1911 

13 

1943 

1975 

2007 

2040 

2073 

2107 

2141 

2175 

2209 

2244 

14 

2279 

2314 

2350 

2386 

2422 

2459 

2496 

2533 

2571 

2609 

15 

2647 

2686 

2725 

2764 

2803 

2843 

2883 

2924 

2965 

3006 

16 

3048 

3090 

3132 

3174 

3217 

3261 

3304 

3348 

3392 

3437 

17 

3482 

3527 

3573 

3619 

3665 

3712 

3759 

3807 

3855 

3903 

18 

3951 

4000 

4049 

4099 

4149 

4199 

4250 

4301 

4353 

4403 

19 

4457 

4509 

4562 

4616 

4670 

4724 

4778 

4833 

4888 

4944 

0.20 

5000 

5056 

5113 

5171 

5228 

5286 

5345 

5403 

5463 

5522 

21 

5582 

5643 

5704 

5765 

5826 

5889 

5951 

6014 

6077 

6141 

22 

6205 

6270 

6335 

6400 

6466 

6532 

6599 

6666 

6734 

6802 

23 

6870 

6939 

7008 

7078 

7148 

7219 

7290 

7362 

7434 

7506 

24 

7579 

7652 

7726 

7800 

7875 

7950 

8026 

8102 

8179 

8256 

25 

8333 

8411 

8490 

8569 

8648 

8728 

8809 

8890 

8971 

9053 

26 

9135 

9218 

9301 

9385 

9470 

9554 

9640 

9726 

9812 

9899 

27 

9986 

1007 

1016 

1025 

1034 

1043 

1052 

1061 

1070 

1080 

28 

1089 

1099 

1108 

1117 

1127 

1136 

1146 

1155 

1165 

1175 

29 

1185 

1194 

1204 

1214 

1224 

1234 

1245 

1255 

1265 

1275 

TABLES. 


275 


TABLE  FOR  CALCULATING  THE  DISSOCIATION  CONSTANT. 

Continued. 


m 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.30 

1286 

1296 

1307 

1317 

1328 

1339 

1349 

1360 

1371 

1382 

31 

1393 

1404 

1415 

1426 

1437 

1449 

1460 

1471 

1483 

1494 

32 

1506 

1518 

1529 

1541 

1553 

1565 

1577 

1589 

1601 

1613 

33 

1625 

1638 

1650 

1663 

1675 

1688 

1700 

1713 

1726 

1739 

34 

1752 

1765 

1778 

1791 

1804 

1817 

1831 

1844 

1857 

1871 

35 

1885 

1898 

1912 

1926 

1940 

1954 

1968 

1982 

1996 

2011 

36 

2025 

2040 

2054 

2068 

2083 

2098 

2113 

2128 

2143 

2158 

37 

2173 

2188 

2203 

2219 

2234 

2250 

2266 

2281 

2297 

2313 

38 

2329 

2345 

2361 

2378 

2394 

2410 

2427 

2443 

2460 

2477 

39 

2493 

2510 

2527 

2545 

2562 

2579 

2596 

2614 

2631 

2649 

0.40 

2667 

2685 

2702 

2720 

2739 

2757 

2775 

2793 

2812 

2830 

41 

2849 

2868 

2887 

"2906 

2925 

2944 

2963 

2983 

3002 

3022 

42 

3041 

3061 

3081 

3101 

3121 

3141 

3162 

3182 

3203 

3223 

43 

3244 

3265 

3286 

3307 

3328 

3349 

3371 

3392 

3414 

3435 

44 

3457 

3479 

3501 

3523 

3546 

3568 

3591 

3613 

3636 

3659 

45 

3682 

3705 

3728 

3752 

3775 

3799 

3822 

3846 

3870 

3894 

46 

3919 

3943 

3967 

3992 

4017 

4042 

4067 

4092 

4117 

4142 

47 

4168 

4194 

4219 

4245 

4271 

4298 

4324 

4351 

4377 

4404 

48 

4431 

4458 

4485 

4512 

4540 

4568 

4595 

4613 

4651 

4680 

49 

4708 

4736 

4765 

4794 

4823 

4852 

4881 

4911 

4940 

4970 

0.50 

5000 

5030 

5060 

5091 

5121 

5152 

5183 

5214 

5245 

5277 

51 

5308 

5340 

5372 

5404 

5436 

5469 

5501 

5534 

5567 

5600 

52 

5633 

5667 

5701 

5734 

5768 

5803 

5837 

5871 

5906 

5941 

53 

5977 

6012 

6048 

6083 

6119 

6155 

6192 

6228 

6265 

6302 

54 

6339 

6377 

6414 

6452 

6490 

6528 

6566 

6605 

6644 

6683 

55 

6722 

6762 

6801 

6841 

6882 

6922 

6963 

7003 

7044 

7086 

56 

7127 

7169 

7211 

7253 

7296 

7339 

7382 

7425 

7468 

7512 

57 

7556 

7600 

7645 

7689 

7734 

7779 

7825 

7871 

7917 

7963 

58 

8010 

8056 

8103 

8151 

8199 

8246 

8295 

8343 

8392 

8441 

59 

8490 

8540 

8590 

8640 

8691 

8741 

8792 

8844 

8896 

8948 

0.60 

9000 

9053 

9106 

9159 

9213 

9267 

9321 

9375 

9430 

9485 

61 

9541 

9597 

9653 

9710 

9767 

9824 

9882 

9940 

9998 

1006 

62 

1012 

1018 

1024 

1030 

1036 

1042 

1048 

1054 

1060 

1066 

63 

1073 

1079 

1085 

1092 

1098 

1105 

1111 

1118 

1124 

1131 

64 

1138 

1145 

1151 

1158 

1165 

1172 

1179 

1186 

1193 

1200 

65 

1207 

1214 

1222 

1229 

1236 

1244 

1251 

1258 

1266 

1274 

66 

1281 

1289 

1297 

1304 

1312 

1320 

1328 

1336 

1344 

1352 

67 

1360 

1369 

1377 

1385 

1393 

1402 

1410 

1419 

1428 

1436 

68 

1445 

1454 

1463 

1473 

1482 

1491 

1499 

1508 

1517 

1526 

69 

1536 

1545 

1555 

1564 

1574 

1583 

1593 

1603 

1613 

1623 

276 


TABLES. 


TABLE  FOR  CALCULATING  THE  DISSOCIATION  CONSTANT. 

Continued. 


m 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.70 

1633 

1643 

1654 

1664 

1674 

1685 

1695 

1706 

1717 

1727 

71 

1738 

1749 

1760 

1771 

1783 

1974 

1805 

1817 

1828 

1840 

72 

1851 

1863 

1875 

1887 

1899 

1911 

1924 

1936 

1949 

1961 

73 

1974 

1987 

1999 

2012 

2025 

2039 

2052 

2065 

2079 

2092 

74 

2106 

2120 

2134 

2148 

2162 

2177 

2191 

2206 

2220 

2235 

75 

2250 

2265 

2280 

2296 

2311 

2327 

2342 

2358 

2374 

2390 

76 

2407 

2423  2440 

2456 

2473 

2490 

2508 

2525 

2542 

2560 

77 

2578 

2596  2614 

2632 

2651 

2669 

2688 

2707 

2727 

2746 

78 

2766 

2785  2805 

2825 

2846 

2866 

2887 

2908 

2929  2950 

79 

2972 

2994 

3016 

3038 

3060 

3083 

3106 

3129 

3153 

3176 

0.80 

3200 

3224  3249 

3273 

3298 

3323 

3348 

3374 

3400 

3427 

81 

3453 

3480 

3507 

3535 

3562 

3590 

3619 

3648 

3677 

3706 

82 

3736 

3766 

3796 

3827 

3858 

3889 

3921 

3953 

3986 

4019 

83 

4052 

4086  1  4120 

4155 

4190 

4225 

4262 

4298 

4335 

4372 

84 

4410 

4448 

4487 

4526 

4566 

4606 

4648 

4689 

4731 

4773 

85 

4816 

4860 

4905 

4950 

4995 

5042 

5088 

5136 

5184 

5233 

86 

5283 

5333  5384 

5436 

5489 

5542 

5597 

5652 

5708 

5765 

87 

5822 

5881  5941 

6001 

6063 

6125 

6189 

6253 

6319 

6386 

88 

6453 

6522  !  6593 

6664 

6737 

68H 

6886 

6963 

7041 

7120 

89 

7201 

7283  7367 

7453 

7540 

7629 

7719 

7812 

7906 

8002 

0.90 

8100 

8200  8302 

8406 

8513 

8621 

8732 

8846  8962 

9080 

91 

9201 

9324 

9452 

9581 

9714 

9850 

9989 

1013 

1028 

1043 

92 

1058 

1074 

1090 

1107 

1123 

1141 

1158 

1177 

1196 

1215 

93 

1236 

1256 

1277 

1299 

1321 

1345 

1369 

1393 

1419 

1445 

94 

1473 

1501 

1530 

1560 

1592 

1624 

1658 

1692 

1728 

1766 

95 

1805 

1846 

1888 

1933 

1979 

2027 

2077 

2130 

2185 

2244 

96 

2304 

2368 

2436 

2506 

2582 

2660 

2744 

2833  2928 

3029 

97 

3136 

3251 

3374 

3507 

3649 

3803 

3970 

4150  4347 

4564 

98 

4802 

5005 

5358 

5684 

6052 

6468 

6945 

7493  8134 

8892 

99 

9801 

1091 

1230 

1409 

1647 

1980 

2480 

3313 

4980 

9980 

POSITION  OF  THE  DECIMAL  POINT. 

m- 
m. 

0.0100 
0.0312 
0.0952 
0.271 
0.619 
0.917 
0.991 


TABLES. 


277 


XXI. 

TABLE  OF  INTERNATIONAL  ATOMIC  WEIGHTS. 


Name. 

Sym. 

O  =  16. 

H  =  l. 

Name. 

Sym. 

O  =  16. 

H  =  l. 

Aluminium  .... 
Antimony  
Areon 

Al 
Sb 
A 

27.1 
120.2 
39  9 

26.9 
119.3 
39  6 

Molybdenum.  .  . 
Neodymium.  .  .  . 
Neon   .  .  . 

Mo 

Ne 

96.0 
143.6 
20 

95.3 
142.5 
19  9 

Arsenic 

As 

75  0 

74  4 

Nickel.  .  .  . 

Ni 

58  7 

58  3 

Barium  .  .  . 

RT 

137  4 

136  4 

Nitrogen.  .  . 

N 

14  04 

13  93 

Bismuth. 

Bi 

208  5 

206  9 

Osmium.  . 

Os 

191 

189  6 

Boron 

B 

11 

10  9 

Oxvffen  . 

O 

16  00 

15  88 

Bromine. 

Br 

79  96 

79  36 

Palladium 

Pd 

106  5 

105  7 

Cadmium  
Caesium.  . 

Cd 
Cs 

112.4 
133 

111.6 
132 

Phosphorus.  .  .  . 
Platinum.  .  . 

P 
Pt 

31.0 
194  8 

30.77 
193  3 

Calcium  

Ca 

40  1 

39  8 

Potassium. 

K 

39  15 

38  86 

Carbon  

c 

12  00 

11.91 

Praseodymium  . 

Pr 

140  5 

139  4 

Cerium  

Cp 

140    ' 

139 

Radium      

Ra 

225 

223.3 

Chlorine  

Cl 

35  45 

35  18 

Rhodium  

Rh 

103.0 

102  2 

Chromium  

Cr 

52.1 

51.7 

Rubidium  

Rh 

85.4 

84.8 

Cobalt 

Co 

59  0 

58  56 

Ruthenium 

Rn 

101  7 

100  9 

Columbium  (Ni- 
obium) 

Cb 

94 

93  3 

Samarium  
Scandium        . 

Sm 

So 

150 
44  1 

148.9 
43  8 

Copper 

Cn 

63  6 

63  1 

Selenium 

SP 

79  2 

78  6 

Erbium  .  . 

F, 

166 

164  8 

Silicon 

Si 

28  4 

28  2 

Fluorine.  . 

F 

19 

18  9 

Silver 

AP- 

107  93 

107  12 

Gadolinium.  .  .  . 
Gallium. 

Gd 
G<\ 

156 
70 

155 
69  5 

Sodium  
Strontium. 

Na 

Sr 

23.05 
87  6 

22.88 
86  94 

Germanium.  .  .  . 
Glucinum     (Be- 

Ge 

72.5 

71.9 

Sulphur  
Tantalum     .  .  .  . 

S 
Tfl 

32.06 
183 

31.83 
181  6 

ryllium)  

Gl 

9  1 

9  03 

TP 

127.6 

126  6 

Gold  

Au 

197  2 

195  7 

Terbium 

Tb 

160 

158  8 

Helium. 

HP 

4 

4 

Thallium 

Tl 

204  1 

202  6 

Hydrogen.  .  . 

H 

1  008 

1  000 

Thorium 

Th 

232  5 

230  8 

Indium.    .  . 

In 

114 

113  1 

Thulium 

Tm 

171 

169  7 

Iodine  .  .  . 

T 

126  85 

125  90 

Tin 

Sn 

119  0 

118  1 

Indium  

Tr 

193  0 

191  5 

Titanium 

Ti 

48  1 

47  7 

Iron 

FP 

55  9 

55  5 

Tungsten 

W 

184  0 

182  6 

Krypton  

K 

81  8 

81  2 

Uranium  . 

TT 

238  5 

236  7 

Lanthanum.  .  .  . 

La 

138  9 

137  9 

Vanadium 

V 

51  2 

50  8 

Lead.  . 

Ph 

206  9 

205  35 

Xenon 

x 

128 

127 

Lithium.  .  .  . 

T.i 

7  03 

6  98 

Ytterbium 

Yb 

173  o 

171  7 

Magnesium.  .  .  . 

Mg 

24.36 

24.18 

Yttrium.  

Yt 

89  0 

88.3 

Manganese. 

Mn 

55  0 

54  6 

Zinc 

7iTl 

65  4 

64  9 

Mercury  

He 

200.0 

198.5 

Zirconium  

7/r 

90.6 

89.9 

278 


TABLES. 


XXII. 

LOGARITHMS  OF  NUMBERS. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

42 

11 

414 

453 

492 

531 

569 

607 

645 

682 

719 

755 

38 

12 

792 

828 

864 

899 

934 

969 

1004 

1038 

1072 

1106 

35 

13 

1139 

1173 

1206 

1239 

1271 

1303 

335 

367 

399 

430 

32 

14 

461 

492 

523 

553 

584 

614 

644 

673 

703 

732 

30 

15 

761 

790 

818 

847 

875 

903 

931 

959 

987 

2014 

28 

16 

2041 

206  3 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

279 

26 

17 

304 

330 

355 

380 

405 

430 

455 

480 

504 

529 

25 

18 

553 

577 

601 

625 

648 

672 

695 

718 

742 

765 

24 

19 

788 

810 

833 

856 

878 

900 

923 

945 

967 

989 

22 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

21 

21 

222 

243 

263 

254 

304 

324 

345 

365 

385 

404 

20 

22 

424 

444 

464 

4S3 

502 

522 

541 

560 

579 

598 

19 

23 

617 

636 

655 

674 

692 

711 

729 

747 

766 

784 

24 

802 

820 

838 

856 

874 

892 

909 

927 

945 

962 

18 

25 

979 

997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

17 

26 

4150 

4166 

183 

200 

216 

232 

249 

265 

281 

298 

16 

27 

314 

330 

346 

362 

378 

393 

409 

425 

440 

456 

28 

472 

487 

502 

518 

533 

548 

564 

579 

594 

609 

15 

29 

624 

639 

654 

669 

683 

698 

713 

728 

742 

757 

30 

771 

786 

800 

814 

829 

843 

857 

871 

886 

900 

14 

31 

914 

928 

942 

955 

969 

983 

997 

5011 

5024 

5038 

32 

5051 

5065 

5079 

5092 

5105 

5119 

5132 

145 

159 

172 

13 

33 

185 

198 

211 

224 

237 

250 

263 

276 

289 

302 

34 

315 

328 

340 

353 

366 

378 

391 

403 

416 

428 

35 

441 

453 

465 

478 

490 

502 

515 

527 

539 

551 

12 

36 

563 

575 

587 

599 

611 

623 

635 

647 

658 

670 

37 

682 

694 

705 

717 

729 

740 

752 

763 

775 

786 

38 

798 

809 

821 

832 

843 

855 

866 

877 

888 

899 

39 

911 

922 

933 

944 

955 

966 

977 

988 

999 

6010 

11 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

117 

41 

128 

138 

149 

159 

170 

180 

191 

201 

212 

222 

42 

232 

243 

253 

263 

274 

284 

294 

304 

314 

325 

43 

335 

345 

355 

365 

375 

385 

395 

405 

415 

425 

10 

44 

435 

444 

454 

464 

474 

484 

493 

503 

513 

522 

45 

532 

542 

551 

561 

571 

580 

590 

599 

609 

618 

46 

628 

637 

646 

656 

665 

675 

684 

693 

702 

712 

47 

721 

730 

739 

749 

758 

767 

776 

785 

794 

803 

48 

,812 

821 

830 

839 

848 

857 

866 

875 

884 

893 

9 

49 

902 

911 

920 

928 

937 

946 

955 

964 

972 

981 

50 

990 

998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

51 

7076 

7084 

093 

101 

110 

118 

126 

135 

143 

152 

52 

160 

168 

177 

185 

193 

202 

210 

218 

226 

235 

53 

243 

251 

259 

267 

275 

284 

292 

300 

308 

316 

8 

54 

324 

332 

340 

348 

356 

364 

372 

380 

388 

396 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLES. 


279 


LOGARITHMS  OF  NUMBERS—  (.Continued). 


0 

i 

2 

3 

4   |  5 

6 

7 

8 

9 

Diff. 

55 

7404 

7412 

7419 

7427 

7435  .7443  7451 

7459 

7466 

7474 

8 

56 

482 

490 

497 

505 

513 

520  528 

536 

543   551 

57 

559 

566 

574 

582 

589 

597   604 

612 

619 

627 

58 

634 

642 

649 

657 

664 

672 

679 

686 

694 

701 

59 

709 

716 

723 

731 

738 

745 

752 

760 

767 

774 

60 

782 

789 

796 

803 

810 

818 

825 

832 

839 

846 

61 

853 

860 

868 

875 

882 

.  889 

896 

903 

910 

917 

7 

62 

924 

931 

938 

945 

952 

959 

966 

973 

980 

987 

63 

993 

8000 

8007 

8014 

8021 

8028 

8035 

8041 

8048 

8055 

64 

8062 

069 

075 

082 

089 

096 

102 

109 

116 

122 

65 

129 

136 

142 

149 

156 

162 

169 

176 

182 

189 

66 

195 

202 

209 

215 

222   228 

235 

241 

248 

254 

67 

261 

267 

274 

2SO 

287   293 

299   306  312 

319 

68 

325 

331 

338 

344 

351 

357 

363 

370 

376 

382 

69 

388 

395 

401 

407 

414 

420 

426 

432 

439 

445 

70 

451 

457 

463 

470 

476 

482 

488 

494 

500 

506 

71 

513 

519 

525 

531 

537 

543 

549 

555 

561 

567 

6 

72 

573 

579 

585 

591 

597 

603 

609 

615 

621 

627 

73 

633 

639 

645 

651 

657 

663 

669 

675 

681 

686 

74 

692 

698 

704 

710 

716 

722 

727 

733 

739 

745 

75 

751 

756 

762 

768 

774 

779 

785 

791 

797 

802 

76 

803 

814 

820 

825 

831 

837 

842 

848 

854 

859 

77 

865 

871 

876 

882 

887 

893 

899 

904 

910 

915 

78 

921 

927 

932 

938 

943 

949 

954 

960 

965 

971 

79 

976 

982 

987 

993 

998 

9004 

9009 

9015 

9020 

9025 

80 

9031 

9036 

9042 

9047 

9053 

058 

063 

069 

074 

079 

81 

085 

090 

096 

101 

106 

112 

117 

122 

128 

133 

82 

138 

143 

149 

154 

159 

165 

170 

175 

180 

186 

83 

191 

196 

201 

206 

212 

217 

222 

227 

232 

238 

84 

243 

248 

253 

258 

263 

269 

274 

279 

284 

289 

85 

294 

299 

304 

309 

315 

320 

325 

330 

335 

340 

86 

345 

350 

355 

360 

365  370 

375 

380 

3S5 

390 

5 

87 

395 

400 

405 

410 

415 

420 

425 

430 

435 

440 

88 

445   450 

455 

460 

465 

469 

474 

479 

4S4 

489 

89 

494   499 

504 

509 

513 

518 

523 

528 

533 

538 

90 

542 

547 

552 

557 

562 

566 

571 

576 

581 

586 

91 

590 

595 

600 

605 

609 

614 

619 

624 

628 

633 

92 

638 

643 

647 

652 

657 

661 

666 

671 

675 

680 

93 

6?5 

689 

694 

699 

703 

708 

713 

717 

722 

727 

94 

731 

736 

741 

745 

750 

754 

759 

763 

768 

773 

95 

777 

782 

786 

791 

795 

800 

805 

809 

814 

818 

96 

823 

827 

832 

836 

841 

845 

850 

854 

859 

863 

97 

868 

872 

877 

881 

886 

890 

894 

899 

903 

908 

98 

912 

917 

921 

926 

930 

934 

939 

943 

948 

952 

99 

956 

961 

965 

969 

974 

978 

983 

987 

991 

996 

4 

0 

1 

2 

3 

4 

5 

6     7 

8 

9 

INDEX. 


A. 

PAGE 

Apparatus,  Boiling-point 68,  78 

Dielectric  Constant 219 

Freezing-point 70 

Heat  of  combustion 113 

Heat  of  Naturalization 107 

Heat  of  Solution 109 

Heat  of  Vaporization 99 

Solubility 235 

Spectrophotoraetric 135 

Volume  Measuring 13 

B. 

Balance 1 

Care  of 3 

Inequality  of  Arms 7 

Sensitiveness  of 6 

Basicity  of  Acids 181 

Battery 231 

Boiling-point  Apparatus 78 

Elevation  of 77 

Method 78 

Bridge-wire,  Calibration  of 167 

Burettes,  Calibration  of 17 

C. 

Calorimeter 86 

Cane-sugar,  Inversion  of 243 

281 


282  INDEX. 

PAGB 

Catalysis  of  Methyl  Acetate 245 

Cell,  Clark  Standard 183 

Helmholtz 186 

Weston 186 

Cells,  Concentration 203 

Conductivity 168 

Conductivity,  Equivalent 178 

Molecular 160 

Specific 160 

Current,  Measurement  of 209 

Sources  of .  156 


D. 

Density .  20 

of  Gases 27 

(Method  of  Dumas) 28 

(Method  of  V.  Meyer) 30 

of  Liquids 23 

of  Solids 20 

Dielectric  Constant,  Measurement  of 219 

Dissociation  Constant 179 

Degree  of 179 

by  Freezing-point  Method 76 

E. 

Electrical  Units 154 

Electrodes,  Preparing 199 

Normal 196 

Electrometer 231 

Capillary 187 

Key 231 

Electromotive  Force 183 

Measurement  of 192 

Electroscope 225 

Eudiometer,  Calibration  of 18 

Expansion,  Coefficient  of 60 

F. 

Fluid,  Flow  of 42 

Freezing-point,  Apparatus 70 


INDEX.  283 

PAGE 

Freezing-point,  Depression  of 70 

Method  .  ,  70 


H. 

Heat  of  Combustion 113 

Dilution 112 

Formation 128 

Fusion 96 

Hydration Ill 

Neutralization 107 

Solidification 98 

Solution .  109 

Vaporization 99 

Heating  Vessel 85 


I. 

Induction  Coil 171 

lonization  Current,  Measurement  of 233 

K. 
Kinetics,  Chemical 242 

L. 
Lamp  for  Homogeneous  Light 149 

M. 

Measuring-flasks,  Calibration  of 16 

Melting-point 67 

Molecular  Volumes  of  Liquids 63 

Weight,  Longinescu  Method 82 

P. 

Partition  Coefficient 239 

Polarimeter 144 

Laurent 145 

Lippich 147 

Potential  Differences .195 


284  INDEX. 

R. 

PAGE 

Radioactivity,  Measurement  of 225 

Reaction,  First  Order 243 

Second  Order , 246 

Refraction  Constants 143 

Refractometer,  Pulfrich 138 

Resistance 159 

Boxes 161 

Capacity 173 

Rotation  Dispersion 152 

Molecular 151 

Specific 151 


S. 

Saponification  of  Ethyl  Acetate 246 

Solubility  by  Conductivity  Method 181 

Solubility,  Determination  of 237 

Solution  Pressure 203 

Specific  Gravity 20 

Specific  Heat,  of  Solids 84 

of  Liquids 93 

Spectra  Absorption 132 

Spectroscope 129 

Adjustment  of 130 

Spectrophotometry 133 

Surfape  Tension,  Measurement  of 52 

and  Molecular  Weight 54 


T. 

Tables 259 

Telephone .172 

Temperature  Coefficient 185 

Regulator 36 

Thermo-chemistry  .  . 104 

Thermometer,  Calibration  of 57 

Comparison  with  Standard 56 

Correction  for  Unheated  Stem 57 

Fixed  Points  of 58 

Mercury : .  .  .  .  ;  56 


INDEX.  285 

PAG* 

Thermostats 34 

Transition  Points 247 

Dilatometric  Method 253 

Electrical             "       254 

Solubility            "       , 248 

Tensimetric         "       251 

Transport  Numbers 212 

Tubes,  Observing 149 

V. 

Viscosity   42 

Measurement  of 46 

Voltameter,  Copper 211 

Silver .  209 

Volumes,  Apparatus  for  Measuring 13 

W. 

Water,  Pure 177 

Wave-lengths,  Reduction  of  Scale-readings  to  . 131 

Weighing  by  Vibrations 4 

Weighings,  Reduction  to  Vacuo 8 

Wheatstone's  Bridge 163 


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*  Descriptive  General  Chemistry 8vo,  3  oo 

Treadwell's  Qualitative  Analysis.     (Hall.) 8vo,  3  oo 

Quantitative  Analysis.     (Hall.) 8vo,  4  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Van  Deventer's  Physical  Chemistry  for  Beginners.     (Boltwood.) i2mo,  i  50 

*  Walke's  Lectures  on  Explosives. 8-0,  4  oo 

Washington's  Manual  of  the  Chemical  Analysis  of  Rocks 8"o,  2  oo 

Wassermann's  Immune  Sera :  Haemolysins,  Cytotoxins,  and  Precipitins.    (Bol- 
duan.)  i2mo,  i  oo 

Well's  Laboratory  Guide  in  Qualitative  Chemical  Analysis 8vo,  i  50 

Short  Course  in  Inorganic  Qualitative  Chemical  Analysis  for  Engineering 

Students _. i2mo,  i  50 

Text-book  of  Chemical  Arithmetic i2mo,  i  25 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

Wilson's  Cyanide  Processes I2mo,  i  50 

Chlorination  Process 1 2ino,  i  50 

Wulling's    Elementary    Course    in  Inorganic,  Pharmaceutical,  and  Medical 

Chemistry i2mo,  2  oo 

CIVIL  ENGINEERING. 

BRIDGES    AND    ROOFS.       HYDRAULICS.       MATERIALS    OF    ENGINEERING. 
RAILWAY  ENGINEERING. 

Baker's  Engineers'  Surveying  Instruments i2mo,  3  oo 

Bixby's  Graphical  Computing  Table Paper  19^X241  inches.  25 

**  Burr's  Ancient  and  Modern  Engineering  and  the  Isthmian  Canal.     (Postage, 

27  cents  additional.) 8vo,  3  50 

Comstock's  Field  Astronomy  for  Engineers 8vo,  2  50 

Davis's  Elevation  and  Stadia  Tables 8vo,  i  oo 

Elliott's  Engineering  for  Land  Drainage 12010,  i  50 

Practical  Farm  Drainage , i2mo,  i  oo 

*Fiebeger's  Treatise  on  Civil  Engineering 8vo,  5  oo 

Folwell's  Sewerage.     (Designing  and  Maintenance.) 8vo,  3  oo 

Freitag's  Architectural  Engineering.     2d  Edition,  Rewritten 8vo,  3  50 

French  and  Ives's  Stereotomy 8vo,  2  50 

Goodhue's  Municipal  Improvements i2mo,  i  75 

Goodrich's  Economic  Disposal  of  Towns'  Refuse 8vo,  3  50 

Gore's  Elements  of  Geodesy 8vo,  2  50 

Hayford's  Text-book  of  Geodetic  Astronomy 8vo,  3  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  so 

5 


Howe's  Retaining  Walls  for  Earth i2mo,  i  25 

Johnson's  (J.  B.)  Theory  and  Practice  of  Surveying Small  8vo,  4  oo 

Johnson's  (L.  J.)  Statics  by  Algebraic  and  Graphic  Methods 8vo,  2  oo 

Laplace's  Philosophical  Essay  on  Probabilities.    (Truscott  and  Emory.) .  i2mo,  2  oo 

Mahan's  Treatise  on  Civil  Engineering.     (1873.)     (Wood.) 8vo,  5  oo 

*  Descriptive  Geometry 8vo,  i  50 

Merriman's  Elements  of  Precise  Surveying  and  Geodesy 8vo,  2  50 

Elements  of  Sanitary  Engineering 8vo,  2  oo 

Merriman  and  Brooks's  Handbook  for  Surveyors i6mo,  morocco,  2  oo 

Nugent's  Plane  Surveying 8vo,  3  50 

Ogden's  Sewer  Design i2mo,  2  oo 

Patton's  Treatise  on  Civil  Engineering 8vo  half  leather,  7  50 

Reed's  Topographical  Drawing  and  Sketching 4 to,  5  oo 

Rideal's  Sewage  and  the  Bacterial  Purification  of  Sewaf_<; 8vo,  3  50 

Siebert  and  Biggin's  Modern  Stone-cutting  and  Masonry 8vo,  i  50 

Smith's  Manual  of  Topographical  Drawing.     (McMillan.) 8vo,  2  50 

Sondericker's  Graphic  Statics,  with  Applications  to  Trusses,  Beams,  and  Arches. 

8vo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

*  Trautwine's  Civil  Engineer's  Pocket-book i6mo,  morocco,  5  oo 

Wait's  Engineering  and  Archi  ectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo,  5  oo 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo 

Warren's  Stereotomy — Problems  in  Stone-cutting 8vo,  2  50 

Webb's  Problems  in  the  Use  and  Adjustment  of  Engineering  Instruments. 

i6mo,  morocco,  i   25 

*  Wheeler  s  Elementary  Course  of  Civil  Engineering 8vo,  4  oo 

Wilson's  Topographic  Surveying 8vo,  3  50 

BRIDGES  AND  ROOFS. 

Boiler's  Practical  Treatise  on  the  Construction  of  Iron  Highway  Bridges .  .  8ro,  2  oo 

*  Thames  River  Bridge 4to,  paper,  5  oo 

Burr's  Course  on  the  Stresses  in  Bridges  and  Roof  Trusses,  Arched  Ribs,  and 

Suspension  Bridges 8vo,  3  50 

Burr  and  Falk's  Influence  Lines  for  Bridge  and  Roof  Computations.  .  .  .8vo,  3  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  II Small  4to,  10  oo 

Foster's  Treatise  on  Wooden  Trestle  Bridges 4to,  5  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50 

Greene's  Roof  Trusses 8vo,  i  25 

Bridge  Trusses 8vo,  2  50 

Arches  in  Wood,  Iron,  and  Stone 8vo,  2  50 

Howe's  Treatise  on  Arches 8vo,  4  oo 

Design  of  Simple  Roof-trusses  in  Wood  and  Steel 8vo,  2  oo 

Johnson,  Bryan,  and  Turneaure's  Theory  and  Practice  in  the  Designing  of 

Modern  Framed  Structures Small  4to,  10  oo 

Merriman  and  Jacoby's  Text-book  on  Roofs  and  Bridges: 

Part  I.     Stresses  in  Simple  Trusses 8vo,  2  50 

Part  II.     Graphic  Statics 8vo,  2  50 

Part  HI.     Bridge  Design , 8vo,  2  50 

Part  IV.     Higher  Structures 8vo,  2  50 

Morison's  Memphis  Bridge 4to,  10  oo 

Waddell's  De  Pontibus,  a  Pocket-book  for  Bridge  Engineers.  .  i6mo,  morocco,  3  oo 

Specifications  for  Steel  Bridges WA'lti       '    I2mo'  x  *5 

Wood's  Treatise  on  the  Theory  of  the  Construction  of  Bridges  and  Roofs .  .  8vo,  2  cc 
Wright's  Designing  of  Draw-spans : 

Part  I.     Plate-girder  Draws 8vo,  2  50 

Part  H.     Riveted-truss  and  Pin-connected  Long-span  Draws 8vo,  2  50 

Two  parts  in  one  volume 8vo,  3  50 

6 


HYDRAULICS. 

Bazin's  Experiments  upon  the  Contraction  of  the  Liquid  Vein  Issuing  from 

an  Orifice.     (Trautwine.) 8vo,  2  oo 

Bovey's  Treatise  on  Hydraulics 8vo,  5  oo 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Diagrams  of  Mean  Velocity  of  Water  in  Open  Channels paper,  i  50 

Coffin's  Graphical  Solution  of  Hydraulic  Problems i6mo,  morocco,  2  50 

Fla trier's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Folwell's  Water-supply  Engineering 8vo,  4  oo 

Frizell's  Water-power 8vo,  5  oo 

Fuertes's  Water  and  Public  Health ' i2mo,  i  50 

Water-filtration  Works ' tamo,  2  50 

Ganguillet  and  Kutter's  General  Formula  for  the  Uniform  Flow  of  Water  in 

Rivers  and  Other  Channels.     (Bering  and  Trautwine.) 8vo,  4  oo 

Hazen's  Filtration  of  Public  Water-supply- 8vo,  3  oo 

Hazlehurst's  Towers  and  Tanks  for  Water- works 8vo,  2  50 

Herschel's  115  Experiments  on  the  Carrying  Capacity  of  Large,  Riveted,  Metal 

Conduits 8vo,  2  oo 

Mason's  Water-supply.     (Considered  Principally  from  a  Sanitary  Standpoint.) 

8vo,  4  oo 

Merriman's  Treatise  on  Hydraulics 8vo,  5  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Schuyler's   Reservoirs  for   Irrigation,   Water-power,   and   Domestic   Water- 
supply Large  8vo,  5  oo 

**  Thomas  and  Watt's  Improvement  of  Rivers.     (Post,  440.  additional.). 4to,  6  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Wegmann's  Design  and  Construction  of  Dams 4to,  5  oo 

Water-supply  of  the  City  of  New  York  from  1658  to  1895 4to,  10  oo 

Williams  and  Hazen's  Hydraulic  Tables 8vo,  i  50 

Wilson's  Irrigation  Engineering Small  8vo,  4  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 

Elements  of  Analytical  Mechanics 8vo,  3  oo 

MATERIALS  OF  ENGINEERING. 

Baker's  Treatise  en  Masonry  Construction 8vo,  5  oo 

Roads  and  Pavements 8vo,  5  oo 

Black's  United  States  Public  Works Oblong  4to,  5  oo 

Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

Byrne's  Highway  Construction 8vo,  5  oo 

Inspection  of  the  Materials  and  Workmanship  Employed  in  Construction. 

i6mo,  3  oo 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  I Small  4to,  7  50 

*Eckel's  Cements,  Limes,  and  Plasters 8vo,  6  oo 

Johnson's  Materials  of  Construction Large  8vo,  6  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics. 8vo,  7  50 

Marten's  Handbook  on  Testing  Materials.     (Henning.)     2  vols 8vo,  7  50 

Merrill's  Stones  for  Building  and  Decoration 8vo,  5  oo 

Merriman's  Mechanics  of  Materials.                                  8vo,  5  oo 

Strength  of  Materials : i2mo,  i  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users i2mo,  2  oo 

Patton's  Practical  Treatise  on  Foundations 8vo,  5  oo 

Richardson's  Modern  Asphalt  Pavements 8vo,  3  oo 

Richey's  Handbook  for  Superintendents  of  Construction i6mo,  mor.,  4  oo 

Rockwell's  Roads  and  Pavements  in  France i2mo,  i  25 

7 


Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Materials  of  Machines i2mo,  i  oo 

Snow's  Principal  Species  of  Wood 8vo,  3  50 

Spalding's  Hydraulic  Cement i2mo,  2  oo 

Text-book  on  Roads  and  Pavements i2mo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Materials  of  Engineering.     3  Parts 8vo,  8  oo 

Part  I.     Non-metallic  Materials  of  Engineering  and  Metallurgy 8vo,  2  oo 

Part  II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Thurston's  Text-book  of  the  Materials  of  Construction 8vo,  5  oo 

Tillson's  Street  Pavements  and  Paving  Materials 8vo,  4  oo 

WaddelTs  De  Pontibus.    (A  Pocket-book  for  Bridge  Engineers.).  .i6mo,  mor.,  3  oo 

Specifications  for  Stu  i  Bridges i2mo,  i  25 

Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials,  and  an  Appendix  on 

the  Preservation  of  Timber 8vo,  2  oo 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Wood':;  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  oo 

RAILWAY  ENGINEERING. 

Andrew's  Handbook  for  Street  Railway  Engineers 3x5  inches,  morocco,  i  25 

Berg's  Buildings  and  Structures  of  American  Railroads 4to,  5  oo 

Brook's  Handbook  of  Street  Railroad  Location i6mo,  morocco,  i  50 

Butt's  Civil  Engineer's  Field-book i6mo,  morocco,  2  50 

Crandall's  Transition  Curve i6mo,  morocco,  i  50 

Railway  and  Other  Earthwork  Tables 8vo,  i  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  .  i6mo,  morocco,  5  oo 

Dredge's  History  of  the  Pennsylvania  Railroad:   (1879) Paper,  5  oo 

*  Drinker's  Tunnelling,  Explosive  Compounds,  and  Rock  Drills. 4to,  half  mor.,  25  oo 

Fisher's  Table  of  Cubic  Yards Cardboard,  25 

Godwin's  Railroad  Engineers'  Field-book  and  Explorers'  Guide.  .  .  i6mo,  mor.,  2  50 

Howard's  Transition  Curve  Field-book i6mo,  morocco,  i  50 

Hudson's  Tables  for  Calculating  the  Cubic  Contents  of  Excavations  and  Em- 
bankments  8vo,  i  oo 

Molitor  and  Beard's  Manual  for  Resident  Engineers i6mo,  i  oo 

Nagle's  Field  Manual  for  Railroad  Engineers i6mo,  morocco,  3  oo 

Philbrick's  Field  Manual  for  Engineers i6mo,  morocco,  3  oo 

Searles's  Field  Engineering i6mo,  morocco,  3  oo 

Railroad  Spiral , i6mo,  morocco,  i  50 

Taylor's  Prismoidal  Formulae  and  Earthwork 8vo,  i  50 

*  Trautwine's  Method  of  Calculating  the  Cube  Contents  of  Excavations  and 

Embankments  by  the  Aid  of  Diagrams 8vo,  2  oo 

The  Field  Practice  of  Laying  Out  Circular  Curves  for  Railroads. 

^       I2mo,  morocco,  2  50 

Cross-section  Sheet Paper,  25 

Webb's  Railroad  Construction i6mo,  morocco,  5  oo 

Wellington's  Economic  Theory  of  the  Location  of  Railways Small  8vo,  5  oo 

DRAWING. 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing. 8vo,  3  oo 

*  "                    "                   "        Abridged  Ed 8vo,  150 

Coolidge's  Manual  of  Drawing 8vo,  paper  i  oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  Engi- 
neers  Oblong  4to,  2  50 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo.  2  50 

8 


Hill's  Text-book  on  Shades  and  Shadows,  and  Perspective 8vo,  2  oo 

Jamison's  Elements  of  Mechanical  Drawing 8vo,  2  50 

Advanced  Mechanical  Drawing 8vo,  2  oo 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery -. 8vo,  i  50 

Part  n.     Form,  Strength,  and  Proportions  of  Partg 8vo,  3  oo 

MacCord's  Elements  of  Descriptive  Geometry 8vo,  3  oo 

Kinematics ;  or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i  50 

*  Mahan's  Descriptive  Geometry  and  Stone-cutting 8vo,  i  50 

Industrial  Drawing.     (Thompson.) 8vo,  3  50 

Moyer's  Descriptive  Geometry 8vo,  2  oo 

Reed's  Topographical  Drawing  and  Sketching 4to,  5  oo 

Reid's  Course  in  Mechanical  Drawing ' 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Robinson's  Principles  of  Mechanism ' 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  Manual  of  Topographical  Drawing.     (McMillan.) 8vo,  2  50 

Warren's  Elements  of  Plane  and  Solid  Free-hand  Geometrical  Drawing.  i2mo,  i  oo 

Drafting  Instruments  and  Operations i2mot  i  25 

Manual  of  Elementary  Projection  Drawing i2mo,  i  59 

Manual  of  Elementary  Problems  in  the  Linear  Perspective  of  Form  and 

Shadow i2mo,  i  oo 

Plane  Problems  in  Elementary  Geometry i2mo,  i  25 

Primary  Geometry •  . . .  i2mo,  75 

Elements  of  Descriptive  Geometry,  Shadows,  and  Perspective 8vo,  3  50 

General  Problems  of  Shades  and  Shadows 8vo,  3  oo 

Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Problems,  Theorems,  and  Examples  in  Descriptive  Geometry 8vo,  2  50 

Weisbach's  Kinematics  and  Power  of  Transmission.    (Hermann  and  Klein)8vo,  5  oo 

Whelpley's  Practical  Instruction  in  the  Ait  of  Letter  Engraving i2mo,  2  oo 

Wilson's  (H.  M.)  Topographic  Surveying 8vo,  3  50 

Wilson's  (V.  T.)  Free-hand  Perspective 8vo,  2  50 

Wilson's  (V.  T.)  Free-hand  Lettering 8vo,  i  oo 

Woolf 's  Elementary  Course  in  Descriptive  Geometry Large  8vo,  3  oo 


ELECTRICITY  AND  PHYSICS. 

Anthony  and  Brackett's  Text-book  of  Physics.     (Magie.) Small  8vo,  3  oo 

Anthony's  Lecture-notes  on  the  Theory  of  Electrical  Measurements.  .  .  .i2mo,  i  oo 

Benjamin's  History  of  Electricity. 8vo,  3  oo 

Voltaic  Cell 8vo,  3  oo 

Classen's  Quantitative  Chemical  Analysis  by  Electrolysis.     (Boltwood.).8vo,  3  oo 

Crehore  and  Squier's  Polarizing  Photo-chronograph 8vo,  3  oo 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  i6mo,  morocco,  5  oo 
Dolezalek's    Theory   of   the    Lead   Accumulator    (Storage    Battery).      (Von 

Ende.) I2mo,  2  50 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.) 8vo,  4  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power I2mo,  3  oo 

Gilbert's  De  Magnete.     (Mottelay.).  . .- 8vo,  2  50 

Hanchett's  Alternating  Currents  Explained i2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  '2  50 

Holman's  Precision  of  Measurements 8vo,  2  oo 

Telescopic   Mirror-scale  Method,  Adjustments,  and  Tests.  . .  .Large  8vo,  75 

Kinzbrunner's  Testing  of  Continuous-Current  Machines 8vo,  2  oo 

Landauer's  Spectrum  Analysis.     (Tmgle.) 8vo,  3  oo 

Le  Chatelien's  High-temperature  Measurements.  (Boudouard — Burgess.)  I2mo,  3  oo 

Lob's  Electrolysis  and  Electrosynthesis  of  Organic  Compounds.  (Lorenz.)  i2mo,  i  oo 

9 


*  Lyons's  Treatise  on  Electromagnetic  Phenomena.  Vols.  I.  and  II.  8vo,  each,    6  oo 

*  Michie's  Elements  of  Wave  Motion  Relating  to  Sound  and  Light 8vo,    4  oo 

Niaudet's  Elementary  Treatise  on  Electric  Batteries.     (Fishback.) i2mo, 

*  Rosenberg's  Electrical  Engineering.     (Haldane  Gee — Kinzbrunner.).  .  .8vo, 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     Vol.  1 8vo, 

Thurston's  Stationary  Steam-engines 8vo, 

*  Tillman's  Elementary  Lessons  in  Heat 8vo, 


Tory  and  Pitcher's  Manual  of  Laboratory  Physics Small  8vo, 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 

LAW. 

*  Davis's  Elements  of  Law 8vo,  2  50 

*  Treatise  on  the  Military  Law  of  United  States 8vo,  7  oo 

*  Sheep,  7  50 

Manual  for  Courts-martial i6mo,  morocco,  i  50 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo,  5  oo 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo 

Winthrop's  Abridgment  of  Military  Law I2mo,  2  50 

MANUFACTURES. 

Bernadou's  Smokeless  Powder — Nitro-cellulose  and  Theory  of  the  Cellulose 

Molecule I2mo,  2  5* 

Bolland's  Iron  Founder i2mo,  2  50 

"The  Iron  Founder,"  Supplement i2mo,  2  50 

Encyclopedia  of  Founding  and  Dictionary  of  Foundry  Terms  Used  in  the 

Practice  of  Moulding : . . .  i2mo,  3  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Effront's  Enzymes  and  their  Applications.     (Prescott.) 8vo,  3  oo 

Fitzgerald's  Boston  Machinist i2mo,  i  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Hopkin's  Oil-chemists'  Handbook 8vo,  3  oo 

Keep's  Cast  Iron 8vo,  2  50 

Leach's  The  Inspection  and  Analysis  of  Feod  with  Special  Reference  to  State 

Control Large  8vo,  7  50 

Matthews's  The  Textile  Fibres 8vo,  3  50 

Metcalf's  Steel.     A  Manual  for  Steel-users i2mo,  2  oo 

Mstcalfe's  Cost  of  Manufactures — And  the  Administration  of  Workshops  8vo,  5  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Morse's  Calculations  used  in  Cane-sugar  Factories i6mo,  morocco,  i  50 

*  Reisig's  Guide  to  Piece-dyeing 8vo,  25  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Press-working  of  Metals 8vo,  3  oo 

Spalding's  Hydraulic  Cement i2tno,  2  oo 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses.    . .  .  i6mo,  morocco,  3  oo 

Handbook  for  Sugar  Manufacturers  and  their  Chemists.  .  i6mo,  morocco,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Manual  of  Steam-boilers,  their  Designs,  Construction  and  Opera- 
tion  8vo,  5  oo 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo 

Ware's  Manufacture  of  Sugar.     (In  press.) 

West's  American  Foundry  Practice I2mo,  2  50 

Moulder's  Text-book i2mo,  2  50 

10 


Wolff's  Windmill  as  a  Prime  Mover 8vo,    3  oe 

Wood's  Rustless  Coatings:   Corrosion  and  Electrolysis  of  Iron  and  Steel.  .8vo,    4  oo 


MATHEMATICS. 

Baker's  Elliptic  Functions 8vo,    I  50 

*  Bass's  Elements  of  Differential  Calculus i2mo,    4  oo 


Briggs's  Elements  of  Plane  Analytic  Geometry 121110, 

Compton's  Manual  of  Logarithmic  Computations i2mo, 

Davis's  Introduction  to  the  Logic  of  Algebra 8vo, 

*  Dickson's  College  Algebra Large  i2mo, 

*  Introduction  to  the  Theory  of  Algebraic  Equations Large  12 mo, 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo, 

Halsted's  Elements  of  Geometry 8vo, 

Elementary  Synthetic  Geometry J 8vo, 


oo 
50 
50 
50 
25 
50 
75 
50 
Rational  Geometry ' I2mo,  75 

*  Johnson's  (J.  B.)  Three-place  Logarithmic  Tables:   Vest-pocket  size. paper,         15 

100  copies  for    5  oo 

*  Mounted  on  heavy  cardboard,  8  X 10  inches,         25 

10  copies  for    2  oo 

Johnson's  (W.  W.)  Elementary  Treatise-  on  Differential  Calculus.  .Smah  8vo,    3  oo 
Johnson's  (W.  W.)  Elementary  Treatise  on  the  Integral  Calculus. Small  8vo,     i  50 

Johnson's  (W.  W.)  Curve  Tracing  in  Cartesian  Co-ordinates i2mo,     i  oo 

Johnson's  (W.  W.)  Treatise  on  Ordinary  and  Partial  Differential  Equations. 

Small  8vo,    3  50 
Johnson's  (W.  W.)  Theory  of  Errors  and  the  Method  of  Least  Squares  i2mo,     i  50 

*  Johnson's  (W.  W.)  Theoretical  Mechanics i2rao,    3  oo 

Laplace's  Philosophical  Essay  on  Probabilities.     (Truscott  and  Emory.) .  i2mo,    2  oo 

*  Ludlow  and  Bass.     Elements  of  Trigonometry  and  Logarithmic  and  t)ther 

Tables 8vo,    3  oo 

Trigonometry  and  Tables  published  separately Each,    2  oo 

*  Ludlow's  Logarithmic  and  Trigonometric  Tables 8vo,    i  oo 

Maurer's  Technical  Mechanics .• 8vo,    4  oo 

Merriman  and  Woodward's  Higher  Mathematics.  , 8vo,    5  oo 

Merriman's  Method  of  Least  Squares 8vo,    2  oo 

Rice  and  Johnson's  Elementary  Treatise  on  the  Differential  Calculus. .  Sm.  8vo,    3  oo 

Differential  and  Integral  Calculus.     2  vols.  in  one Small  8vo,    2  50 

Wood's  Elements  of  Co-ordinate  Geometry 8vo,    2  oo 

Trigonometry:  Analytical,  Plane,  and  Spherical i2mo,    i  oo 


MECHANICAL  ENGINEERING. 

MATERIALS  OF  ENGINEERING,  STEAM-ENGINES  AND  BOILERS. 

Bacon's  Forge  Practice i2mo,  i  50 

Baldwin's  Steam  Heating  for  Buildings 121110,  2  50 

Barr's  Kinematics  of  Machinery. 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

*  "  "  "        Abridged  Ed 8vo,     150 

Benjamin's  Wrinkles  and  Recipes i2mo,    2  oo 

Carpenter's  Experimental  Engineering 8vo,    6  oo 

Heating  and  Ventilating  Buildings 8vo,    4  oo 

Gary's  Smoke  Suppression  in  Plants  using  Bituminous  Coal.     (In  Prepara- 
tion.) 

Clerk's  Gas  and  Oil  Engine Small  8vo,    4  oo 

Coolidge's  Manual  of  Drawing ; 8vo,  paper,     i  oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  En- 
gineers  Oblong  4to,    2  50 

11 


Cromwell's  Treatise  on  Toothed  Gearing i2mo,  i  50 

Treatise  on  Belts  and  Pulleys i2mo,  i  50 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Flather's  Dynamometers  and  the  Measurement  of  Power. 12 mo,  3  oo 

Rope  Driving 12010,  2  oo 

Gill's  Gas  and  Fuel  Analysis  for  Engineers i2mo,  i  25 

Hall's  Car  Lubrication I2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Button's  The  Gas  Engine 8vo,  5  oo 

Jamison's  Mechanical  Drawing 8vo,  2  50 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

Kent's  Mechanical  Engineers'  Pocket-book i6mo,  morocco,  5  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Leonard's  Machine  Shop,  Tools,  and  Methods.  . . 8vo,  4  oo 

*Lorenz's  Modern  Refrigerating  Machinery.     (Pope,  Haven,  and  Dean.)  .  .8vo,  4  oo 

MacCord's  Kinematics;   or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i  50 

Mahan's  Industrial  Drawing.     (Thompson.) 8vo,  3  50 

Poole  s  Calorific  Power  of  Fuels 8vo,  3  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richard's  Compressed  Air » I2mo,  i  50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism , 8vo,  3  oo 

Smith's  Press-working  of  Metals 8vo,  3  oo 

Thurston's   Treatise   on   Friction  and   Lost  Work   in   Machinery  and   Mill 

Wof k 8vo,  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics .  i2mo,  i  oo 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Weisbach's    Kinematics    and    the    Power    of    Transmission.     (Herrmann — 

Klein.) • 8vo,  5  oo 

Machinery  of  Transmission  and  Governors.     (Herrmann — Klein.).  .8vo,  5  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 


MATERIALS   OF    ENGINEERING. 

Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering.    6th  Edition. 

Reset 8vo,  7  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Johnson's  Materials  of  Construction 8vo,  6  oo 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  50 

Martens's  Handbook  on  Testing  Materials.     (Henning.) 8vo,  7  5° 

Merriman's  Mechanics  of  Materials.                                8vo,  5  oo 

Strength  of  Materials i2mo,  i  oo 

Metcalf's  Steel.     A  manual  for  Steel-users I2mo.  2  «o 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Materials  of  Machines I2mo,  i  oo 

Thurston's  Materials  of  Engineering 3  vols.,  8vo,  8  oo 

Part  H.     Iran  and  Steel 8vo,  3  50 

Part  HI.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo»  3  5° 

Text-book  of  the  Materials  of  Construction. 8vo,  5  oo 

12 


Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials  and  an  Appendix  on 

the  Preseivation  of  Timber 8vo,    2  oO 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,    3  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Ste«L 8vo,    4  oo 


STEAM-ENGINES  AND  BOILERS. 


Berry's  Temperature-entropy  Diagram izmo,  i  25 

Carnot's  Reflections  on  the  Motive  Power  of  Heat.     (Thurston.) izmo,  i  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  .  .  .i6mo,  mor.,  5  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Goss's  Locomotive  Sparks 8vo,  2  oo 

Hemenway's  Indicator  Practice  and  Steam-engine  Economy i2mo,  2  oo 

Button's  Mechanical  Engineering  of  Power  Plants 8vo,  5  oo 

Heat  and  Heat-engines 8vo,  5  oo 

Kent's  Steam  boiler  Economy 8vo,  4  oo 

Kneass's  Practice  and  Theory  of  the  Injector 8vo,  i  50 

MacCord's  Slide-valves 8vo,  2  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Peabody's  Manual  of  the  Steam-engine  Indicator i2mo.  i  50 

Tables  of  the  Properties  of  Saturated  Steam  and  Other  Vapors.  ....  .8vo,  i  oo 

Thermodynamics  of  the  Steam-engine  and  Other  Heat-engines 8vo,  5  oo 

Valve-gears  for  Steam-engines 8vo,  2  50 

Peabody  and  Miller's  Steam-boilers 8vo,  4  oo 

Pray's  Twenty  Years  with  the  Indicator Large  8vo,  2  50 

Pupin's  Thermodynamics  of  Reversible  Cycles  in  Gases  and  Saturated  Vapors. 

(Osterberg.) i2mo,  i  25 

Reagan's  Locomotives:  Simple  Compound,  and  Electric 12 mo,  2  50 

Rontgen's  Principles  of  Thermodynamics.     (Du  Bois.). 8vo,  5  oo 

Sinclair's  Locomotive  Engine  Running  and  Management 12 mo,  2  oo 

Smart's  Handbook  of  Engineering  Laboratory  Practice i2mo,  2  50 

Snow's  Steam-boiler  Practice. 8vo,  3  oo 

Spangier's  Valve-gears 8vo,  2  50 

Notes  on  Thermodynamics i2mo,  i  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thurston's  Handy  Tables 8vo,  i  50 

Manual  of  the  Steam-engine 2  vols.,  8vo,  10  oo 

Part  I.     History,  Structure,  and  Theory 8vo,  6  oo 

Part  II.     Design,  Construction,  and  Operation 8vo,  6  oo 

Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indicator  and 

the  Prony  Brake 8vo,  5  oo 

Stationary  Steam-engines 8vo,  2  50 

Steam-boiler  Explosions  in  Theory  and  in  Practice i2mo,  i  50 

Manual  of  Steam-boilers,  their  Designs,  Construction,  and  Operation 8vo,  5  oo 

Weisbach's  Heat,  Steam,  and  Steam-engines.     (Du  Bois.) 8vo,  5  oo 

Whitham's  Steam-engine  Design 8vo,  5  oo 

Wilson's  Treatise  on  Steam-boilers.     (Flather.) i6mo,  2  so 

Wood's  Thermodynamics,  Heat  Motors,  and  Refrigerating  Machines.  .  .8vo,  4  oo 


MECHANICS  AND  MACHINERY. 

Barr's  Kinematics  of  Machinery ,8vo,  2  50 

Bovcy's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Chase's  The  Art  of  Pattern-making •. . . .  Z2mo,  2  50 

Church!s  Mechanics  of  Engineering 8vo,  6  oo 

15 


Church's  Notes  and  Examples  in  Mechanics 8vo>  2  oo 

Compton's  First  Lessons  in  Metal-working i2mo,  i  50 

Compton  and  De  Groodt's  The  Speed  Lathe i2mo,  i  50 

Cromwell's  Treatise  on  Toothed  Gearing i2mo,  ;  50 

Treatise  on  Belts  and  Pulleys i2mo,  i  50 

Dana's  Text-book  of  Elementary  Mechanics  for  Colleges  and  Schools.  .  i2mo,  i  50 

Dingey's  Machinery  Pattern  Making i2mo,  2  oo 

Dredge's  Record  of  the  Transportation  Exhibits  Building  of  the  World's 

Columbian  Exposition  of  1893 4to  half  morocco,  5  oo 

Du  Bois's  Elementary  Principles  of  Mechanics: 

Vol.      I.     Kinematics 8vo,  3  50 

Vol.    II.     Statics 8vo,  4  oo 

VoL  HI.     Kinetics 8vo,  3  50 

Mechanics  of  Engineering.     Vol.    I Small  4to,  7  50 

VoL  II Small  4to,  10  oo 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Fitzgerald's  Boston  Machinist i6mo,  i  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Rope  Driving i2mo,  2  oo 

Goss's  Locomotive  Sparks 8vo,  2  oo 

Hall's  Car  Lubrication 12100,  i  oo 

Holly's  Art  of  Saw  Filing i8mo,  75 

James's  Kinematics  of  a  Point  and  the  Rational  Mechanics  of  a  Particle.  Sm.8vo,2  oo 

*  Johnson's  (W.  W.)  Theoretical  Mechanics i2mo,  3  oo 

Johnson's  (L.  J.)  Statics  by  Graphic  and  Algebraic  Methods 8vo,  2  oo 

Jones's  Machine  Design : 

Part   I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vc,  3  oo 

Kerr's  Power  and  Power  Transmission , 8vo,  2  oo 

Lanza's  Applied  Mechanics 8vo,  7  50 

Leonard's  Machine  Shop,  Tools,  and  Methods 8vo,  4  oo 

*Lorenz's  Modern  Refrigerating  Machinery.      (Pope,  Haven,  and  Dean.). 8vo,  4  oo' 

MacCord*s  Kinematics;  or,  Practical  Mechanism 8vo,  5  oo 

Velocity  Diagrams 8vo,  i  50 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

*  Elements  of  Mechanics i2mo,  i  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Reagan's  Locomotives:  Simple,  Compound,  and  Electric i2mo,  2  50 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richards's  Compressed  Air i2mo,  i  50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     VoL  1 8vo,  2  50 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Sinclair's  Locomotive-engine  Running  and  Management i2tno,  2  oo 

Smith's  (O.)  Press-working  of  Metals 8vo,  3  oo 

Smith's  (A.  W.)  Materials  of  Machines I2mo,  i  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thurston's  Treatise  on  Friction  and  Lost  V/ork  in    Machinery  and    Mill 

Work 8vo,  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics. 

I2H10,  I    OO 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Weisbach's  Kinematics  and  Power  of  Transmission.  ( Herrmann — Klein. ) .  8vo ,  5  oo 

Machinery  of  Transmission  and  Governors.  (Herrmann — Klein. ).8vo,  5  oo 

Wood's  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Principles  of  Elementary  Mechanics I2mo,  i  25 

Turbines 8vo,  2  50 

The  World's  Columbian  Exposition  of  1893 4to,  I  oo 

14 


METALLURGY. 

Egleston's  Metallurgy  of  Silver,  Gold,  and  Mercury: 

Vol.    t     Silver .8vo,  7  50 

Vol.  II.     Gold  and  Mercury 8vo,  7  So 

**  Iles's  Lead-smelting.     (Postage  9  cents  additional.) I2mo,  2  50 

Keep's  Cast  Iron 8vo,  2  50 

Earnhardt's  Practice  of  Ore  Dressing  in  Europe 8vo,  i  50 

Le  Chatelier's  High- temperature  Measurements.  (Boudouard — Burgess. )i2mo,  3  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users-     i2mo,  2  oo 

Smith's  Materials  of  Machines i2mo,  i  oo 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo.  8  oo 

Part   H.     Iron  and  Steel 8vo.  3  5<> 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Hike's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 

MINERALOGY. 

Barringer's  Description  of  Minerals  of  Commercial  Value.    Oblong,  morocco,  2  50 

Boyd's  Resources  of  Southwest  Virginia • 8vo,  3  oo 

Map  of  Southwest  Virignia Pocket-book  form.  2  oo 

Brush's  Manual  of  Determinative  Mineralogy.     (Penfield.) 8vo.  4  oo 

Chester's  Catalogue  of  Minerals 8vo,  paper,  i  oo 

Cloth,  i  25 

Dictionary  of  the  Names  of  Minerals 8vo,  3  50 

Dana's  System  of  Mineralogy. Large  8vo,  half  leather,  12  50 

First  Appendix  to  Dana's. New  "  System  of  Mineralogy." Large  8vo,  i  oo 

Text-book  of  Mineralogy 8vo,  4  oo 

Minerals  and  How  to  Study  Them i2mo,  50 

Catalogue  of  American  Localities  of  Minerals Large  8vo,  oo 

Manual  of  Mineralogy  and  Petrography i2mo,  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects i2mo,  oo 

Eakle's  Mineral  Tables 8vo,  25 

Egleston's  Catalogue  of  Minerals  and  Synonyms 8vo,  50 

Hussak's  The  Determination  of  Rock-forming  Minerals.    (Smith.). Small  8vo,  oo 

Merrill's  Non-metallic  Minerals:  Their  Occurrence  and  Uses 8vo,  4  oo 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo  paper,  o  50 
Rosenbusch's   Microscopical  Physiography   of   the   Rock-making  Minerals. 

(Iddings.) 8vo,  5  oo 

*  Tillman's  Text-book  of  Important  Minerals  and  Rocks 8vo.  2  oo 

Williams's  Manual  of  Lithology 8vo,  3  oo 

MINING. 

Beard's  Ventilation  of  Mines I2mo.  2  50 

Boyd's  Resources  of  Southwest  Virginia 8vo.  3  oo 

Map  of  Southwest  Virginia Pocket  book  form,  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects i2mo.  i  oo 

*  Drinker's  Tunneling,  Explosive  Compounds,  and  Rock  Drills.  ,4to,hf.  mor..  25  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Fowler's  Sewage  Works  Analyses. .  . .  „ 12010,  2  oo 

Goodyear 's  Coal-mines  of  the  Western  Coast  of  the  United  States i2mo,  2  50 

Ihlseng's  Manual  of  Mining 8vo*  s  oo 

**  Iles's  Lead-smelting.     (Postage  pc.  additional.) _ I2mo.  2  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe , 8vo,  i  50 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo,  2  oo 

*  Walke's  Lectures  on  Explosives Svo,  4  oo 

Wilson's  Cyanide  Processes I2mo.,  i  50 

Chlorination  Process I2mo,  i  50 

15 


Wilson's  Hydraulic  and  Placer  Mining i2mo,  2  oo 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation T2mo,  i  25 

SANITARY  SCIENCE. 

Bashore's  Sanitation  of  a  Country  House I2mo,  i  oo 

FolwelTs  Sewerage.     (Designing,  Construction,  and  Maintenance.) 8vo,  3  09 

Water-supply  Engineering SYO,  4  oo 

Fuertes's  Water  and  Public  Health. i2mo,  i  50 

Water-filtration  Works I2mo,  2  50 

Gerhard's  Guide  to  Sanitary  House-inspection i6mo,  i  oo 

Goodrich's  Economic  Disposal  of  Town's  Refuse Demy  8vo,  3  50 

Hazen's  Filtration  of  Public  Water-supplies 8vo,  3  oo 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control 8vo,  7  50 

Mason's  Water-supply.  (Considered  principally  from  a  Sanitary  Standpoint)  8vo,  4  oo 

Examination  of  Water.     (Chemical  and  Bacteriological.) I2mo,  i  25 

Merriman's  Elements  of  Sanitary  Eng'.neering 8vo,  2  oo 

Ogden's  Sewer  Design i2mo,  2  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
ence to  Sanitary  Water  Analysis I2mo,  i  25 

*  Price's  Handbook  on  Sanitation i2mo,  i  50 

Richards's  Cost  of  Food.     A  Study  in  Di»taries i2mo,  i  oo 

Cost  of  Living  as  Modified  by  Sanitaiy  Science i2mo,  i  oo 

Richards  and  Woodman's  Air,  Water,  and  Food  from  a  Sanitary  Stand- 
point  8vo,  2  oo 

*  Richards  and  Williams's  The  Dietary  Computer 8vo,  i  50 

Rideal's  Sewage  and  Bacterial  Purification  of  Sewage 8vo,  3  50 

Turneaure  and  Russell's  Public  Water-supplies .- 8vo,  5  oo 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) i2mo,  i  oo 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

Woodhull's  Notes  on  Military  Hygiene i6mo,  i  50 

MISCELLANEOUS. 

De  Fursac's  Manual  of  Psychiatry.     (Rosanoff  and  Collins.) Large  12 mo,  2  50 

Emmons's  Geological  Guide-book  of  the  Rocky  Mountain  Excursion  of  the 

International  Congress  of  Geologists Large  8vo,  i  50 

Fen-el's  Popular  Treatise  on  the  Winds 8vo,  4  oo 

Haines's  American  Railway  Management i2mo,  2  50 

Mott's  Composition,  Digestibility,  and  Nutritive  Value  of  Food.  Mounted  chart,  i  25 

Fallacy  of  the  Present  Theory  of  Sound i6mo,  i  oo 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute,  1824-1894-  -Small  8vo,  3  oo 

Rostoski's  Serum  Diagnosis.     (Bolduan.) i2mo,  i  oo 

Rotherham's  Emphasized  New  Testament. Large  8vo,  2  oo 

Steel's  Treatise  on  the  Diseases  of  the  Dog 8vo,  3  50 

Totten's  Important  Question  in  Metrology 8vo,  2  50 

The  World's  Columbian  Exposition  of  1893 4*o,  i  oo 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) i2mo,  i  o< 

Winslow's  Elements  of  Applied  Microscopy i2mo,  i  50 

Worcester  and  Atkinson.     Small  Hospitals,  Establishment  and  Maintenance; 

Suggestions  for  Hospital  Architecture :  Plans  for  Small  Hospital .  i2mo,  i  25 

HEBREW  AND  CHALDEE  TEXT-BOOKS. 

Green's  Elementary  Hebrew  Grammar xamo,  i 

Hebrew  Chrestomathy. 8vo'  a  °' 

Gesenius's  Hebrew  and  Chaldee  Lexicon  to   the  Old  Testament  Scriptures. 

(Tregelles.) Small  4to,  half  morocco,  5  o< 

Letter's  Hebrew  Bible 8vo'  *  2g 

16 


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